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Zlatko Bacic - One of the best experts on this subject based on the ideXlab platform.
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accurate quantum calculations of translation rotation Eigenstates in electric dipole coupled h2o c60 assemblies
Chemical Physics Letters, 2017Co-Authors: Peter M Felker, Zlatko BacicAbstract:Abstract We present methodology for variational calculation of the 6 n -dimensional translation-rotation (TR) Eigenstates of assemblies of n H2O@C60 moieties coupled by dipole-dipole interactions. We show that the TR Hamiltonian matrix for any n can be constructed from dipole-dipole matrix elements computed for n = 2 . We present results for linear H2O@C60 assemblies. Two classes of Eigenstates are revealed. One class comprises excitations of the 1 11 rotational level of H2O. The lowest-energy 1 11 -derived eigenstate for each assembly exhibits significant dipole ordering and shifts down in energy with the assembly size.
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electric dipole coupled h2o c60 dimer translation rotation Eigenstates from twelve dimensional quantum calculations
Journal of Chemical Physics, 2017Co-Authors: Peter M Felker, Zlatko BacicAbstract:We report on variational solutions to the twelve-dimensional (12D) Schrodinger equation appertaining to the translation-rotation (TR) Eigenstates of H2O@C60 dimer, associated with the quantized “rattling” motions of the two encapsulated H2O molecules. Both H2O and C60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR Eigenstates of H2O@C60 monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR Eigenstates reported by us recently [P. M. Felker and Z. Bacic, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H2O@C60 dimer for two values of the water dipole moment and for various dimer geometries. 12D TR Eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of Eigenstates, distinguished by th...
Peter M Felker - One of the best experts on this subject based on the ideXlab platform.
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accurate quantum calculations of translation rotation Eigenstates in electric dipole coupled h2o c60 assemblies
Chemical Physics Letters, 2017Co-Authors: Peter M Felker, Zlatko BacicAbstract:Abstract We present methodology for variational calculation of the 6 n -dimensional translation-rotation (TR) Eigenstates of assemblies of n H2O@C60 moieties coupled by dipole-dipole interactions. We show that the TR Hamiltonian matrix for any n can be constructed from dipole-dipole matrix elements computed for n = 2 . We present results for linear H2O@C60 assemblies. Two classes of Eigenstates are revealed. One class comprises excitations of the 1 11 rotational level of H2O. The lowest-energy 1 11 -derived eigenstate for each assembly exhibits significant dipole ordering and shifts down in energy with the assembly size.
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electric dipole coupled h2o c60 dimer translation rotation Eigenstates from twelve dimensional quantum calculations
Journal of Chemical Physics, 2017Co-Authors: Peter M Felker, Zlatko BacicAbstract:We report on variational solutions to the twelve-dimensional (12D) Schrodinger equation appertaining to the translation-rotation (TR) Eigenstates of H2O@C60 dimer, associated with the quantized “rattling” motions of the two encapsulated H2O molecules. Both H2O and C60 moieties are treated as rigid and the cage-cage geometry is taken to be fixed. We consider the TR Eigenstates of H2O@C60 monomers in the dimer to be coupled by the electric dipole-dipole interaction between water moieties and develop expressions for computing the matrix elements of that interaction in a dimer basis composed of products of monomer 6D TR Eigenstates reported by us recently [P. M. Felker and Z. Bacic, J. Chem. Phys. 144, 201101 (2016)]. We use these expressions to compute TR Hamiltonian matrices of H2O@C60 dimer for two values of the water dipole moment and for various dimer geometries. 12D TR Eigenstates of the dimer are then obtained by filter diagonalization. The results reveal two classes of Eigenstates, distinguished by th...
Marcos Rigol - One of the best experts on this subject based on the ideXlab platform.
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Eigenstate Thermalization in a Locally Perturbed Integrable System.
arXiv: Statistical Mechanics, 2020Co-Authors: Marlon Brenes, Tyler Leblond, John Goold, Marcos RigolAbstract:Eigenstate thermalization is widely accepted as the mechanism behind thermalization in generic isolated quantum systems. Using the example of a single magnetic defect embedded in the integrable spin-1/2 XXZ chain, we show that locally perturbing an integrable system can give rise to eigenstate thermalization. Unique to such setups is the fact that thermodynamic and transport properties of the unperturbed integrable chain emerge in properties of the Eigenstates of the perturbed (nonintegrable) one. Specifically, we show that the diagonal matrix elements of observables in the perturbed Eigenstates follow the microcanonical predictions for the integrable model, and that the ballistic character of spin transport in the integrable model is manifest in the behavior of the off-diagonal matrix elements of the current operator in the perturbed Eigenstates.
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entanglement entropy of Eigenstates of quadratic fermionic hamiltonians
Physical Review Letters, 2017Co-Authors: Lev Vidmar, Lucas Hackl, Eugenio Bianchi, Marcos RigolAbstract:: In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993)PRLTAO0031-900710.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is S_{ave}≃lnD_{A}-(1/2)D_{A}^{2}/D for 1≪D_{A}≤sqrt[D], where D_{A} and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S⟩ of all Eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models lnD_{A}-(lnD_{A})^{2}/lnD≤⟨S⟩≤lnD_{A}-[1/(2ln2)](lnD_{A})^{2}/lnD. Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S⟩
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thermalization and its mechanism for generic isolated quantum systems
Nature, 2008Co-Authors: Marcos Rigol, Vanja Dunjko, Maxim OlshaniiAbstract:It is demonstrated that an isolated generic quantum many-body system does relax to a state well described by the standard statistical mechanical prescription. The thermalization happens at the level of individual Eigenstates, allowing the computation of thermal averages from knowledge of any eigenstate in the microcanonical energy window. An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies1,2 of the problem have become possible, stimulating theoretical interest3,4,5,6,7. In generic isolated systems, non-equilibrium dynamics is expected8,9 to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible10. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete11. Some recent studies4,5 even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual Eigenstates, as first proposed by Deutsch12 and Srednicki13. A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result.
David A Huse - One of the best experts on this subject based on the ideXlab platform.
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many body localization and thermalization in quantum statistical mechanics
Annual Review of Condensed Matter Physics, 2015Co-Authors: Rahul Nandkishore, David A HuseAbstract:We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose Eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and...
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Testing whether all Eigenstates obey the Eigenstate Thermalization Hypothesis
Physical Review E, 2014Co-Authors: Tatsuhiko N Ikeda, David A HuseAbstract:We ask whether the Eigenstate Thermalization Hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, {\it every} eigenstate is thermal. We examine expectation values of few-body operators in highly-excited many-body Eigenstates and search for `outliers', the Eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases, and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the Eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.
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testing whether all Eigenstates obey the eigenstate thermalization hypothesis
Physical Review E, 2014Co-Authors: Tatsuhiko N Ikeda, David A HuseAbstract:: We ask whether the eigenstate thermalization hypothesis (ETH) is valid in a strong sense: in the limit of an infinite system, every eigenstate is thermal. We examine expectation values of few-body operators in highly excited many-body Eigenstates and search for "outliers," the Eigenstates that deviate the most from ETH. We use exact diagonalization of two one-dimensional nonintegrable models: a quantum Ising chain with transverse and longitudinal fields, and hard-core bosons at half-filling with nearest- and next-nearest-neighbor hopping and interaction. We show that even the most extreme outliers appear to obey ETH as the system size increases and thus provide numerical evidences that support ETH in this strong sense. Finally, periodically driving the Ising Hamiltonian, we show that the Eigenstates of the corresponding Floquet operator obey ETH even more closely. We attribute this better thermalization to removing the constraint of conservation of the total energy.
A Scardicchio - One of the best experts on this subject based on the ideXlab platform.
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clustering of nonergodic Eigenstates in quantum spin glasses
Physical Review Letters, 2017Co-Authors: C L Baldwin, C R Laumann, A ScardicchioAbstract:: The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum p-spin models of the spin-glass theory, Eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic Eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.
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Clustering of Nonergodic Eigenstates in Quantum Spin Glasses
Physical Review Letters, 2017Co-Authors: C L Baldwin, C R Laumann, A ScardicchioAbstract:The two primary categories for eigenstate phases of matter at finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that in the paradigmatic quantum $p$-spin models of spin-glass theory, Eigenstates violate ETH yet are not MBL either. A mobility edge, which we locate to leading order in $1/p$ using the forward-scattering approximation and replica techniques, separates the non-ergodic phase at small transverse field from an ergodic phase at large transverse field. The non-ergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in spin-glass theory. We show that the non-ergodic Eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.
