The Experts below are selected from a list of 113532 Experts worldwide ranked by ideXlab platform
Jozef Strečka - One of the best experts on this subject based on the ideXlab platform.
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Exact Ground States of Frustrated Spin-1 Ising-Heisenberg and Heisenberg Ladders in a Magnetic Field
Acta Physica Polonica A, 2014Co-Authors: Jozef Strečka, Frederic Michaud, Frédéric MilaAbstract:Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. Both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
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Exact Ground States of Frustrated Spin-1 Ising-Heisenberg and Heisenberg Ladders in a Magnetic Field
arXiv: Statistical Mechanics, 2013Co-Authors: Jozef Strečka, Frederic Michaud, Frédéric MilaAbstract:Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
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Intermediate magnetization plateaus in the spin-1/2 Ising-Heisenberg and Heisenberg models on two-dimensional triangulated lattices
Physical Review B, 2013Co-Authors: Jana Cisarova, Frederic Michaud, Frédéric Mila, Jozef StrečkaAbstract:The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices are exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical-quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent, and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model. DOI: 10.1103/PhysRevB.87.054419
Guang-can Guo - One of the best experts on this subject based on the ideXlab platform.
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"Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field.
Physical review letters, 2021Co-Authors: Zhibo Hou, Yan Jin, Hongzhen Chen, Jun-feng Tang, Chang-jiang Huang, Haidong Yuan, Guo-yong Xiang, Guang-can GuoAbstract:The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.
Alistair Savage - One of the best experts on this subject based on the ideXlab platform.
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Foundations of Frobenius Heisenberg categories
arXiv: Representation Theory, 2020Co-Authors: Jonathan Brundan, Alistair Savage, Ben WebsterAbstract:We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical comultiplication and generalized cyclotomic quotients of the category. We use our basis theorem to prove that the Grothendieck ring of the Karoubi envelope of the Frobenius Heisenberg category recovers the lattice Heisenberg algebra associated to the Frobenius algebra.
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Frobenius Heisenberg categorification
Algebraic Combinatorics, 2019Co-Authors: Alistair SavageAbstract:We associate a graded monoidal supercategory $\mathcal{H}\mathit{eis}_{F,k}$ to every graded Frobenius superalgebra $F$ and integer $k$. These categories, which categorify a broad range of lattice Heisenberg algebras, recover many previously defined Heisenberg categories as special cases. In this way, the categories $\mathcal{H}\mathit{eis}_{F,k}$ serve as a unifying and generalizing framework for Heisenberg categorification. Even in the case of previously defined Heisenberg categories, we obtain new, more efficient, presentations of these categories, based on an approach of Brundan. When $k=0$, our construction yields new versions of the affine oriented Brauer category depending on a graded Frobenius superalgebra.
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Twisted Heisenberg Doubles
Communications in Mathematical Physics, 2015Co-Authors: Daniele Rosso, Alistair SavageAbstract:We introduce a twisted version of the Heisenberg double, constructed from a twisted Hopf algebra and a twisted pairing. We state a Stone–von Neumann type theorem for a natural Fock space representation of this twisted Heisenberg double and deduce the effect on the algebra of shifting the product and coproduct of the original twisted Hopf algebra. We conclude by showing that the quantum Weyl algebra, quantum Heisenberg algebras, and lattice Heisenberg algebras are all examples of the general construction.
Hiroaki Nakajima - One of the best experts on this subject based on the ideXlab platform.
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Noncommutative superspace and super Heisenberg group
Journal of High Energy Physics, 2008Co-Authors: Ee Chang-young, Hoil Kim, Hiroaki NakajimaAbstract:In this paper, we consider noncommutative superspace in relation with super Heisenberg group. We construct a matrix representation of super Heisenberg group and apply this to the two-dimensional deformed = (2,2) superspace that appeared in string theory. We also construct a toy model for non-centrally extended `super Heisenberg group'.
Zhibo Hou - One of the best experts on this subject based on the ideXlab platform.
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"Super-Heisenberg" and Heisenberg Scalings Achieved Simultaneously in the Estimation of a Rotating Field.
Physical review letters, 2021Co-Authors: Zhibo Hou, Yan Jin, Hongzhen Chen, Jun-feng Tang, Chang-jiang Huang, Haidong Yuan, Guo-yong Xiang, Guang-can GuoAbstract:The Heisenberg scaling, which scales as N^{-1} in terms of the number of particles or T^{-1} in terms of the evolution time, serves as a fundamental limit in quantum metrology. Better scalings, dubbed as "super-Heisenberg scaling," however, can also arise when the generator of the parameter involves many-body interactions or when it is time dependent. All these different scalings can actually be seen as manifestations of the Heisenberg uncertainty relations. While there is only one best scaling in the single-parameter quantum metrology, different scalings can coexist for the estimation of multiple parameters, which can be characterized by multiple Heisenberg uncertainty relations. We demonstrate the coexistence of two different scalings via the simultaneous estimation of the magnitude and frequency of a field where the best precisions, characterized by two Heisenberg uncertainty relations, scale as T^{-1} and T^{-2}, respectively (in terms of the standard deviation). We show that the simultaneous saturation of two Heisenberg uncertainty relations can be achieved by the optimal protocol, which prepares the optimal probe state, implements the optimal control, and performs the optimal measurement. The optimal protocol is experimentally implemented on an optical platform that demonstrates the saturation of the two Heisenberg uncertainty relations simultaneously, with up to five controls. As the first demonstration of simultaneously achieving two different Heisenberg scalings, our study deepens the understanding on the connection between the precision limit and the uncertainty relations, which has wide implications in practical applications of multiparameter quantum estimation.
