Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Applied Mathematics and Computational Mechanics

Time evolution of the haldane state after a quantum quench

Dariusz Woźniak, A. Drzewiński, G. Kamieniarz

Published Dec 1, 2014• 1 citation
Publisher

Abstract

In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated.The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified.The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been investigated.

DOI
10.17512/jamcm.2014.4.20

Related papers

Time Evolution of the Magnetic Chains with Uniaxial Anisotropy

Dariusz Woźniak, A. Drzewiński, G. Kamieniarz

In the framework of the matrix product states representation the eect of the single-ion anisotropy on the time evolution of the initial state after a sudden quench of the local magnetic eld has been investigated.The overlap of the initial and time-evolved states, so called the Loschmidt echo, magnetization proles and correlation functions are presented.

Acta Physica Polonica A•Feb 1, 2015•3 citations

Relaxation Dynamics in the Spin-1 Heisenberg Antiferromagnetic Chain after a Quantum Quench of the Uniaxial Anisotropy

Dariusz Woźniak, A. Drzewiński, G. Kamieniarz

In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated.Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives.An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured.In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.

Acta Physica Polonica A•Dec 1, 2016•5 citations

Ultraviolet dynamics from ground-state overlap in the Kondo model

C. D. Pelwan, Izak Snyman

We consider a quantum quench from the strongly correlated ground state of the Kondo model to a Fermi sea. We calculate the overlap between the ground states before and after the quench, as well as the Loschmidt echo, i.e., the transition amplitude between the initial state and the evolved state at a time $t$ after the quench. The overlap is known to determine the dynamics of the echo at large times. We show, in addition, that the overlap depends algebraically on the emergent Kondo length, with a power-law exponent that is the difference of long and short-time contributions that appear in the echo. Our result suggests that, in general, there may be more information contained in the overlap than previously recognized.

arXiv:1812.03692•Physical review. B./Physical review. B•Feb 22, 2019•0 citations

Loschmidt Echo Revivals: Critical and Noncritical

Rouhollah Jafari, Henrik Johannesson

A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point-measuring the time dependence of the overlap between initial and time-evolved states-is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting XY model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears.

arXiv:1612.07046•Physical Review Letters•Jan 5, 2017•110 citations

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Paolo P Mazza, Jean-Marie Stéphan, Elena Canovi +3 more

Abstract The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

arXiv:1509.04666•Journal of Statistical Mechanics Theory and Experiment•Jan 1, 2016•40 citations

Overlap distributions for quantum quenches in the anisotropic Heisenberg chain

Mazza, P., Jean-Marie Stéphan, Canovi, E. +3 more

The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Neel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.

•Jan 1, 2016•44 citations
In the framework of the Matrix Product States representation the effect of a sudden quench of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated.The existence of the non-vanishing string correlations in the limit of a large distance in the Haldane phase has been verified.The overlap of the initial and time-evolved states, the so-called Loschmidt echo, has been investigated.
In the framework of the matrix product state representation the effect of a sudden turning on of the uniaxial anisotropy on the time evolution of the Haldane state has been investigated.Depending on the value of the uniaxial anisotropy parameter, the calculations were derived within (or outside) the region where the Haldane gap survives.An exact expression for the time evolution of the Loschmidt echo has been derived and, moreover, its collapse and revival behaviour was captured.In addition, the non-local order parameter of a time evolving state was tracked, revealing two types of relaxations.
We consider a quantum quench from the strongly correlated ground state of the Kondo model to a Fermi sea. We calculate the overlap between the ground states before and after the quench, as well as the Loschmidt echo, i.e., the transition amplitude between the initial state and the evolved state at a time ttt after the quench. The overlap is known to determine the dynamics of the echo at large times. We show, in addition, that the overlap depends algebraically on the emergent Kondo length, with a power-law exponent that is the difference of long and short-time contributions that appear in the echo. Our result suggests that, in general, there may be more information contained in the overlap than previously recognized.
A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point-measuring the time dependence of the overlap between initial and time-evolved states-is expected to exhibit an accelerated relaxation followed by periodic revivals. We here introduce a new exactly solvable model, the extended Su-Schrieffer-Heeger model, the Loschmidt echo of which provides a counterexample. A parallell analysis of the quench dynamics of the three-site spin-interacting XY model allows us to pinpoint the conditions under which a periodic Loschmidt revival actually appears.
Abstract The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Néel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.
The dynamics after a quantum quench is determined by the weights of the initial state in the eigenspectrum of the final Hamiltonian, i.e. by the distribution of overlaps in the energy spectrum. We present an analysis of such overlap distributions for quenches of the anisotropy parameter in the one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide an overview of the form of the overlap distribution for quenches from various initial anisotropies to various final ones, using numerical exact diagonalization. We show that if the system is prepared in the antiferromagnetic Neel state (infinite anisotropy) and released into a non-interacting setup (zero anisotropy, XX point) only a small fraction of the final eigenstates gives contributions to the post-quench dynamics, and that these eigenstates have identical overlap magnitudes. We derive expressions for the overlaps, and present the selection rules that determine the final eigenstates having nonzero overlap. We use these results to derive concise expressions for time-dependent quantities (Loschmidt echo, longitudinal and transverse correlators) after the quench. We use perturbative analyses to understand the overlap distribution for quenches from infinite to small nonzero anisotropies, and for quenches from large to zero anisotropy.