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Tomaž Prosen - One of the best experts on this subject based on the ideXlab platform.
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Spectral statistics of non hermitian matrices and dissipative quantum chaos
Physical Review Letters, 2021Co-Authors: Tomaž Prosen, Amos ChanAbstract:We propose a measure, which we call the dissipative Spectral Form factor (DSFF), to characterize the Spectral statistics of non-Hermitian (and nonunitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale). Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems, respectively. For dissipative quantum chaotic systems, we show that the DSFF exhibits an exact rotational symmetry in its complex time argument $\ensuremath{\tau}$. Analogous to the Spectral Form factor (SFF) behavior for Gaussian unitary ensemble, the DSFF for GinUE shows a ``dip-ramp-plateau'' behavior in $|\ensuremath{\tau}|$: the DSFF initially decreases, increases at intermediate timescales, and saturates after a generalized Heisenberg time, which scales as the inverse mean level spacing. Remarkably, for large matrix size, the ``ramp'' of the DSFF for GinUE increases quadratically in $|\ensuremath{\tau}|$, in contrast to the linear ramp in the SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that the DSFF takes a constant value, except for a region in complex time whose size and behavior depend on the eigenvalue density. Numerically, we verify the above claims and additionally show that the DSFF for real and quaternion real Ginibre ensembles coincides with the GinUE behavior, except for a region in the complex time plane of measure zero in the limit of large matrix size. As a physical example, we consider the quantum kicked top model with dissipation and show that it falls under the Ginibre universality class and Poisson as the ``kick'' is switched on or off. Lastly, we study Spectral statistics of ensembles of random classical stochastic matrices or Markov chains and show that these models again fall under the Ginibre universality class.
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random matrix Spectral Form factor of dual unitary quantum circuits
Communications in Mathematical Physics, 2021Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:We investigate a class of local quantum circuits on chains of d-level systems (qudits) that share the so-called ‘dual unitarity’ property. In essence, the latter property implies that these systems generate unitary dynamics not only when propagating in time, but also when propagating in space. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over $$\mathrm{SU}(d)$$ , e.g. one concentrated around the identity, after each layer of the circuit. We identify the Spectral Form factor at time t in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of t sites. For general dual unitary circuits of qubits $$(d=2)$$ and a family of their extensions to higher $$d>2$$ , we provide an explicit construction of the commutant and prove that Spectral Form factor exactly matches the prediction of circular unitary ensemble for all t, if only the local 2-qubit gates are different from a SWAP (non-interacting gate).
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Spectral statistics of non hermitian matrices and dissipative quantum chaos
arXiv: Statistical Mechanics, 2021Co-Authors: Tomaž Prosen, Amos ChanAbstract:We propose a measure, which we call the dissipative Spectral Form factor (DSFF), to characterize the Spectral statistics of non-Hermitian (and non-Unitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos, and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy (and time) scale. Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems respectively. For dissipative quantum chaotic systems, we show that DSFF exhibits an exact rotational symmetry in its complex time argument $\tau$. Analogous to the Spectral Form factor (SFF) behaviour for Gaussian unitary ensemble, DSFF for GinUE shows a "dip-ramp-plateau" behavior in $|\tau|$: DSFF initially decreases, increases at intermediate time scales, and saturates after a generalized Heisenberg time which scales as the inverse mean level spacing. Remarkably, for large matrix size, the "ramp" of DSFF for GinUE increases quadratically in $|\tau|$, in contrast to the linear ramp in SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that DSFF takes a constant value except for a region in complex time whose size and behavior depends on the eigenvalue density. Numerically, we verify the above claims and additionally compute DSFF for real and quaternion real Ginibre ensembles. As a physical example, we consider the quantum kicked top model with dissipation, and show that it falls under the universality class of GinUE and Poisson as the `kick' is switched on or off. Lastly, we study Spectral statistics of ensembles of random classical stochastic matrices or Markov chains, and show that these models fall under the class of Ginibre ensemble.
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random matrix Spectral Form factor of dual unitary quantum circuits
arXiv: Mathematical Physics, 2020Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time direction, but also when propagating in the space direction. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over ${\rm SU}(d)$, e.g. one concentrated around the identity, after each layer of the circuit. We identify the Spectral Form factor at time $t$ in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of $t$ sites. For general dual unitary circuits of qubits $(d=2)$ and a family of their extensions to higher $d>2$, we provide explicit construction of the commutant and prove that Spectral Form factor exactly matches the prediction of circular unitary ensemble for all $t$, if only the local 2-qubit gates are different from a SWAP (non-interacting gate). We discuss and partly prove possible extensions of our results to a weaker (more singular) Forms of disorder averaging, as well as to quantum circuits with time-reversal symmetry, and to computing higher moments of the Spectral Form factor.
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exact Spectral Form factor in a minimal model of many body quantum chaos
Physical Review Letters, 2018Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT Spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transForm of Spectral density's two-point function, the Spectral Form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the Spectral Form factor is demonstrated to match RMT for all values of the integer time variable $t$ in the thermodynamic limit. In particular, we rigorously prove RMT Form factor for an odd $t$, while we Formulate a precise conjecture for an even $t$. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.
Prosen Tomaž - One of the best experts on this subject based on the ideXlab platform.
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Spectral properties of three-dimensional Anderson model
2021Co-Authors: Šuntajs Jan, Prosen Tomaž, Vidmar LevAbstract:The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its properties from the perspective of modern numerical approaches. Our main focus is on the quantitative comparison between the level sensitivity statistics and the level statistics. While the Former studies the sensitivity of Hamiltonian eigenlevels upon inserting a magnetic flux, the latter studies the properties of unperturbed eigenlevels. We define two versions of dimensionless conductance, the first corresponding to the width of the level curvature distribution relative to the mean level spacing, and the second corresponding to the ratio of the Heisenberg and the Thouless time obtained from the Spectral Form factor. We show that both conductances look remarkably similar around the localization transition, in particular, they predict a nearly identical critical point consistent with other measures of the transition. We then study some further properties of those quantities: for level curvatures, we discuss particular similarities and differences between the width of the level curvature distribution and the characteristic energy studied by Edwards and Thouless in their pioneering work [J. Phys. C. 5, 807 (1972)]. In the context of the Spectral Form factor, we show that at the critical point it enters a broad time-independent regime, in which its value is consistent with the level compressibility obtained from the level variance. Finally, we test the scaling solution of the average level spacing ratio in the crossover regime using the cost function minimization approach introduced in [Phys. Rev. B. 102, 064207 (2020)]. We find that the extracted transition point and the scaling coefficient agree with those from the literature to high numerical accuracy.Comment: Comments welcom
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Chaos and Ergodicity in Extended Quantum Systems with Noisy Driving
2021Co-Authors: Kos Pavel, Bertini Bruno, Prosen TomažAbstract:We study the time evolution operator in a family of local quantum circuits with random fields in a fixed direction. We argue that the presence of quantum chaos implies that at large times the time evolution operator becomes effectively a random matrix in the many-body Hilbert space. To quantify this phenomenon we compute analytically the squared magnitude of the trace of the evolution operator -- the generalised Spectral Form factor -- and compare it with the prediction of Random Matrix Theory (RMT). We show that for the systems under consideration the generalised Spectral Form factor can be expressed in terms of dynamical correlation functions of local observables in the infinite temperature state, linking chaotic and ergodic properties of the systems. This also provides a connection between the many-body Thouless time $\tau_{\rm th}$ -- the time at which the generalised Spectral Form factor starts following the random matrix theory prediction -- and the conservation laws of the system. Moreover, we explain different scalings of $\tau_{\rm th}$ with the system size, observed for systems with and without the conservation laws.Comment: 7+10 pages, 5 figures, 1 table; v2 improved exposition with the additional section I in S
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Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
'Springer Science and Business Media LLC', 2021Co-Authors: Bertini Bruno, Kos Pavel, Prosen TomažAbstract:We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time direction, but also when propagating in the space direction. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over ${\rm SU}(d)$, e.g. one concentrated around the identity, after each layer of the circuit. We identify the Spectral Form factor at time $t$ in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of $t$ sites. For general dual unitary circuits of qubits $(d=2)$ and a family of their extensions to higher $d>2$, we provide explicit construction of the commutant and prove that Spectral Form factor exactly matches the prediction of circular unitary ensemble for all $t$, if only the local 2-qubit gates are different from a SWAP (non-interacting gate). We discuss and partly prove possible extensions of our results to a weaker (more singular) Forms of disorder averaging, as well as to quantum circuits with time-reversal symmetry, and to computing higher moments of the Spectral Form factor.Comment: 30 pages; v2 rigorous results for spatially inhomogeneous interactions added; v3 extended version, it contains some unproven conjectures not published in CM
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Statistics of the Spectral Form factor in the self-dual kicked Ising model
'American Physical Society (APS)', 2021Co-Authors: Flack Ana, Bertini Bruno, Prosen TomažAbstract:We compute the full probability distribution of the Spectral Form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at long enough times the probability distribution agrees exactly with the prediction of random-matrix theory if one identifies the appropriate ensemble of random matrices. We find that this ensemble is not the circular orthogonal one—composed of symmetric random unitary matrices and associated with time-reversal-invariant evolution operators—but is an ensemble of random matrices on a more restricted symmetric space [depending on the parity of the number of sites this space is either S p(N)/U (N) or O(2N)/O(N)×O(N)]. Even if the latter ensembles yield the same averaged Spectral Form factor as the circular orthogonal ensemble, they show substantially enhanced fluctuations. This behavior is due to a recently identified additional antiunitary symmetry of the self-dual kicked Ising model
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Random matrix Spectral Form factor in kicked interacting fermionic chains
'American Physical Society (APS)', 2021Co-Authors: Roy Dibyendu, Prosen TomažAbstract:We study quantum chaos and Spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle-number conservation $[U(1)]$ symmetry. We analytically show that the Spectral Form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless time which scales with the size $L$ as $mathcal{O}(L^2)$, or $mathcal{O}(L^0)$, in the presence, or absence, of $U(1)$ symmetry, respectively. Using a random phase assumption which essentially requires a long-range nature of the interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the Spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian
Yehao Zhou - One of the best experts on this subject based on the ideXlab platform.
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Note on global symmetry and SYK model
Journal of High Energy Physics, 2019Co-Authors: Junyu Liu, Yehao ZhouAbstract:The goal of this note is to explore the behavior of effective action in the SYK model with general continuous global symmetries. A global symmetry will decompose the whole Hamiltonian of a many-body system to several single charge sectors. For the SYK model, the effective action near the saddle point is given as the free product of the Schwarzian action part and the free action of the group element moving in the group manifold. With a detailed analysis in the free sigma model, we prove a modified version of Peter-Weyl theorem that works for generic spin structure. As a conclusion, we could make a comparison between the thermodynamics and the Spectral Form factors between the whole theory and the single charge sector, to make predictions on the SYK model and see how symmetry affects the chaotic behavior in certain timescales.
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Supersymmetric SYK model and random matrix theory
Journal of High Energy Physics, 2017Co-Authors: Junyu Liu, Yuan Xin, Yehao ZhouAbstract:In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the N = 1 supersymmetric generalization of Sachdev-Ye-Kitaev (SYK) model, a toy model for two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the Spectral Form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic hamiltonian with supersymmetry.
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supersymmetric syk model and random matrix theory
arXiv: High Energy Physics - Theory, 2017Co-Authors: Junyu Liu, Yuan Xin, Yehao ZhouAbstract:In this paper, we investigate the effect of supersymmetry on the symmetry classification of random matrix theory ensembles. We mainly consider the random matrix behaviors in the $\mathcal{N}=1$ supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model, a toy model for the two-dimensional quantum black hole with supersymmetric constraint. Some analytical arguments and numerical results are given to show that the statistics of the supersymmetric SYK model could be interpreted as random matrix theory ensembles, with a different eight-fold classification from the original SYK model and some new features. The time-dependent evolution of the Spectral Form factor is also investigated, where predictions from random matrix theory are governing the late time behavior of the chaotic Hamiltonian with supersymmetry.
Amos Chan - One of the best experts on this subject based on the ideXlab platform.
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Spectral statistics of non hermitian matrices and dissipative quantum chaos
Physical Review Letters, 2021Co-Authors: Tomaž Prosen, Amos ChanAbstract:We propose a measure, which we call the dissipative Spectral Form factor (DSFF), to characterize the Spectral statistics of non-Hermitian (and nonunitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale). Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems, respectively. For dissipative quantum chaotic systems, we show that the DSFF exhibits an exact rotational symmetry in its complex time argument $\ensuremath{\tau}$. Analogous to the Spectral Form factor (SFF) behavior for Gaussian unitary ensemble, the DSFF for GinUE shows a ``dip-ramp-plateau'' behavior in $|\ensuremath{\tau}|$: the DSFF initially decreases, increases at intermediate timescales, and saturates after a generalized Heisenberg time, which scales as the inverse mean level spacing. Remarkably, for large matrix size, the ``ramp'' of the DSFF for GinUE increases quadratically in $|\ensuremath{\tau}|$, in contrast to the linear ramp in the SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that the DSFF takes a constant value, except for a region in complex time whose size and behavior depend on the eigenvalue density. Numerically, we verify the above claims and additionally show that the DSFF for real and quaternion real Ginibre ensembles coincides with the GinUE behavior, except for a region in the complex time plane of measure zero in the limit of large matrix size. As a physical example, we consider the quantum kicked top model with dissipation and show that it falls under the Ginibre universality class and Poisson as the ``kick'' is switched on or off. Lastly, we study Spectral statistics of ensembles of random classical stochastic matrices or Markov chains and show that these models again fall under the Ginibre universality class.
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Spectral statistics in constrained many body quantum chaotic systems
Physical Review Research, 2021Co-Authors: Abhinav Prem, Sanjay Moudgalya, David A Huse, Amos ChanAbstract:The authors study the Spectral Form factor for Floquet random quantum circuits and analytically identify the onset of quantum chaos in many-body systems subject to local constraints, showing that systems with conserved higher moments display subdiffusive dynamics.
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Spectral statistics of non hermitian matrices and dissipative quantum chaos
arXiv: Statistical Mechanics, 2021Co-Authors: Tomaž Prosen, Amos ChanAbstract:We propose a measure, which we call the dissipative Spectral Form factor (DSFF), to characterize the Spectral statistics of non-Hermitian (and non-Unitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos, and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy (and time) scale. Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems respectively. For dissipative quantum chaotic systems, we show that DSFF exhibits an exact rotational symmetry in its complex time argument $\tau$. Analogous to the Spectral Form factor (SFF) behaviour for Gaussian unitary ensemble, DSFF for GinUE shows a "dip-ramp-plateau" behavior in $|\tau|$: DSFF initially decreases, increases at intermediate time scales, and saturates after a generalized Heisenberg time which scales as the inverse mean level spacing. Remarkably, for large matrix size, the "ramp" of DSFF for GinUE increases quadratically in $|\tau|$, in contrast to the linear ramp in SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that DSFF takes a constant value except for a region in complex time whose size and behavior depends on the eigenvalue density. Numerically, we verify the above claims and additionally compute DSFF for real and quaternion real Ginibre ensembles. As a physical example, we consider the quantum kicked top model with dissipation, and show that it falls under the universality class of GinUE and Poisson as the `kick' is switched on or off. Lastly, we study Spectral statistics of ensembles of random classical stochastic matrices or Markov chains, and show that these models fall under the class of Ginibre ensemble.
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Spectral statistics and many-body quantum chaos with conserved charge
Phys.Rev.Lett., 2019Co-Authors: Aaron J. Friedman, Amos Chan, Andrea De Luca, J T ChalkerAbstract:We investigate Spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the Spectral Form factor K(t) analytically for a minimal Floquet circuit model that has a U(1) symmetry encoded via spin-1/2 degrees of freedom. Averaging over an ensemble of realizations, we relate K(t) to a partition function for the spins, given by a Trotterization of the spin-1/2 Heisenberg ferromagnet. Using Bethe ansatz techniques, we extract the “Thouless time” tTh demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for K(t) at t≲tTh. We also report numerical results for K(t) in a generic Floquet spin model, which are consistent with these analytic predictions.
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solution of a minimal model for many body quantum chaos
Physical Review X, 2018Co-Authors: Amos Chan, Andrea De Luca, J T ChalkerAbstract:We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space, and time evolution for a pair of sites is generated by a q2 × q2 random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of the evolution period and to its neighbor on the other side during the second half of the period. We show how dynamical behavior averaged over realizations of the random matrices can be evaluated using diagrammatic techniques and how this approach leads to exact expressions in the large-q limit. We give results for the Spectral Form factor, relaxation of local observables, bipartite entanglement growth, and operator spreading.
Bruno Bertini - One of the best experts on this subject based on the ideXlab platform.
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random matrix Spectral Form factor of dual unitary quantum circuits
Communications in Mathematical Physics, 2021Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:We investigate a class of local quantum circuits on chains of d-level systems (qudits) that share the so-called ‘dual unitarity’ property. In essence, the latter property implies that these systems generate unitary dynamics not only when propagating in time, but also when propagating in space. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over $$\mathrm{SU}(d)$$ , e.g. one concentrated around the identity, after each layer of the circuit. We identify the Spectral Form factor at time t in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of t sites. For general dual unitary circuits of qubits $$(d=2)$$ and a family of their extensions to higher $$d>2$$ , we provide an explicit construction of the commutant and prove that Spectral Form factor exactly matches the prediction of circular unitary ensemble for all t, if only the local 2-qubit gates are different from a SWAP (non-interacting gate).
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random matrix Spectral Form factor of dual unitary quantum circuits
arXiv: Mathematical Physics, 2020Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:We investigate a class of brickwork-like quantum circuits on chains of $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these systems generate unitary dynamics not only when propagating in the time direction, but also when propagating in the space direction. We consider space-time homogeneous (Floquet) circuits and perturb them with a quenched single-site disorder, i.e. by applying independent single site random unitaries drawn from arbitrary non-singular distribution over ${\rm SU}(d)$, e.g. one concentrated around the identity, after each layer of the circuit. We identify the Spectral Form factor at time $t$ in the limit of long chains as the dimension of the commutant of a finite set of operators on a qudit ring of $t$ sites. For general dual unitary circuits of qubits $(d=2)$ and a family of their extensions to higher $d>2$, we provide explicit construction of the commutant and prove that Spectral Form factor exactly matches the prediction of circular unitary ensemble for all $t$, if only the local 2-qubit gates are different from a SWAP (non-interacting gate). We discuss and partly prove possible extensions of our results to a weaker (more singular) Forms of disorder averaging, as well as to quantum circuits with time-reversal symmetry, and to computing higher moments of the Spectral Form factor.
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exact Spectral Form factor in a minimal model of many body quantum chaos
Physical Review Letters, 2018Co-Authors: Bruno Bertini, Pavel Kos, Tomaž ProsenAbstract:The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well-defined classical limit as well as by systems with no classical correspondence, such as locally interacting spins or fermions. Despite great phenomenological success, a general mechanism explaining the emergence of RMT without reference to semiclassical concepts is still missing. Here we provide the example of a quantum many-body system with no semiclassical limit (no large parameter) where the emergence of RMT Spectral correlations is proven exactly. Specifically, we consider a periodically driven Ising model and write the Fourier transForm of Spectral density's two-point function, the Spectral Form factor, in terms of a partition function of a two-dimensional classical Ising model featuring a space-time duality. We show that the self-dual cases provide a minimal model of many-body quantum chaos, where the Spectral Form factor is demonstrated to match RMT for all values of the integer time variable $t$ in the thermodynamic limit. In particular, we rigorously prove RMT Form factor for an odd $t$, while we Formulate a precise conjecture for an even $t$. The results imply ergodicity for any finite amount of disorder in the longitudinal field, rigorously excluding the possibility of many-body localization. Our method provides a novel route for obtaining exact nonperturbative results in nonintegrable systems.
