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Application of Resolvent CCR Algebras to Statistical Mechanics of Bosons on Lattices (Mathematical Aspects of Quantum Fields and Related Topics)

Taku Matsui, Tomohiro Kanda

数理解析研究所講究録Aug 1, 20180 citations

One Parameter Groups Associated with Quantum Girsanov Transformation (Mathematical aspects of quantum fields and related topics)

Mi Ra Lee

数理解析研究所講究録Aug 1, 20190 citations

Continuous extension of the discrete shift translations on one-dimensional quantum lattice systems

Hajime Moriya, Heide Narnhofer

We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems. We explore a specific example provided by a quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system, comparing it with its original discrete shift-translations. Specifically, we demonstrate its explicit dynamical formula, which reveals violations of causality and locality. Furthermore, we prove that this quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system cannot be extended to the one-dimensional quantum spin lattice system via the Jordan-Wigner transformation.We study the continuous extension of discrete shift translations on one-dimensional quantum lattice systems. We explore a specific example provided by a quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system, comparing it with its original discrete shift-translations. Specifically, we demonstrate its explicit dynamical formula, which reveals violations of causality and locality. Furthermore, we prove that this quasi-free C ∗ {C}^{\ast } -flow on the one-dimensional fermion lattice system cannot be extended to the one-dimensional quantum spin lattice system via the Jordan-Wigner transformation.

arXiv:2405.01001Proceedings of the American Mathematical SocietyJul 19, 20240 citations

Connection between continuous and discrete time quantum walks. From D-dimensional lattices to general graphs

Domenico D’Alessandro

arXiv:0902.3496Reports on Mathematical PhysicsAug 1, 201019 citations

Interface states of quantum lattice models(Recent Trends in Infinite Dimensional Non-Commutative Analysis)

Tohru Koma, Bruno Nachtergaele

We review recent results on interface ground states of quantum spin systems.

数理解析研究所講究録Apr 1, 19980 citations

Continuous Matrix Product Ansatz for One-dimensional Fermi Systems

Sangwoo S. Chung

The central topic of this thesis is on the fermionic continuous matrix product states (cMPS) variational ansatz for many-body quantum systems in a one-dimensional (1D) continuum.The matrix product states (MPS) is a variational ansatz which has been tremendously successful for nearly two decades in efficiently approximating groundstate properties of low-dimensional quantum lattice systems.The MPS is intrinsically designed for discrete lattice systems, however, and the cMPS has been introduced in 2010 as a continuum analogue of the MPS, enabling the possibility to directly tackle systems of quantum gases and liquids without resorting to discretization of space.The central topic of this thesis is on the fermionic continuous matrix product states (cMPS) variational ansatz for many-body quantum systems in a one-dimensional (1D) continuum.The matrix product states (MPS) is a variational ansatz which has been tremendously successful for nearly two decades in efficiently approximating groundstate properties of low-dimensional quantum lattice systems.The MPS is intrinsically designed for discrete lattice systems, however, and the cMPS has been introduced in 2010 as a continuum analogue of the MPS, enabling the possibility to directly tackle systems of quantum gases and liquids without resorting to discretization of space.

Jan 1, 20160 citations

On implementation of discrete and continuous shift translations on quantum lattice systems (Mathematical Aspects of Quantum Fields and Related Topics)

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On implementation of discrete and continuous shift translations on quantum lattice systems (Mathematical Aspects of Quantum Fields and Related Topics)

Abstract

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