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

Semi-classical theory for quantum quenches in the O(3) non-linear sigma model

Stefano Evangelisti

Published Aug 17, 2016• 34 citations
OpenAlex

Abstract

Abstract. We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method. ar X iv

Related papers

Semi-classical theory for quantum quenches in the O(3) non-linear sigma model

Stefano Evangelisti

We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method.

arXiv:1210.4028•Journal of Statistical Mechanics Theory and Experiment•Apr 2, 2013•26 citations

Semiclassical theory for quantum quenches in finite transverse Ising chains

Heiko Rieger, Ferenc Iglói

We present a quantitative semiclassical theory for the nonequilibrium dynamics of transverse Ising chains after quantum quenches, in particular, sudden changes of the transverse field strength. We obtain accurate predictions for the quench-dependent relaxation times and correlation lengths, and also about the recurrence times and quasiperiodicity of time-dependent correlations in finite systems with open or periodic boundary conditions. We compare the quantitative predictions of our semiclassical theory (local magnetization, equal-time bulk-bulk and surface-to-bulk correlations, and bulk autocorrelations) with the results from exact free-fermion calculations, and discuss the range of applicability of the semiclassical theory and possible generalizations and extensions.

arXiv:1106.5248•Physical Review B•Oct 19, 2011•133 citations

Quantum quenches and competing orders: II. quantum non-linear sigma model

Ling-Yan Hung, Wenbo Fu, Subir Sachdev A

We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large $N$ limit of a O($N$) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.

•Feb 4, 2014•0 citations

Critical quench dynamics of random quantum spin chains: ultra-slow relaxation from initial order and delayed ordering from initial disorder

Gergö Roósz, Yu-Cheng Lin, Ferenc Iglói

By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, , of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by , and in a finite sample of length L the average magnetization saturates at a size-dependent plateau here the two exponents satisfy the relation . Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until with and then starts to increase until it saturates to an asymptotic value , with . For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable . Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.

arXiv:1611.09495•New Journal of Physics•Feb 16, 2017•7 citations

Quantum Correlations in Field Theory and Integrable Systems

Evangelisti, Stefano

In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will therefore be devoted to the study of the entanglement entropy in one-dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting theory with non perturbative solutions. We derive its bipartite Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap is analysed, both analytically and numerically. In particular it is worth mentioning that the numerical analysis of the entropies of the XYZ model presented in this dissertation has never been published in literature. In the second part of the thesis we study the dynamics of correlators after a quantum quench, preparing the system in a squeezed coherent initial state. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, the latter studied by means of the semi-classical theory, the former by a form-factor approach. Moreover in the last chapter we outline a general result about the dynamics of correlation functions of local observables after a quantum quench. In particular we show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model at long times (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations). For the Transverse Field Ising Chain this result means that its dynamics is described by a Generalized Gibbs Ensemble.

arXiv:1302.5836•Jan 1, 2013•5 citations

Non-equilibrium quantum dynamics after local quenches

Uma Divakaran, Ferenc Iglói, Heiko Rieger

We study the quantum dynamics resulting from preparing a one-dimensional quantum system in the ground state of initially two decoupled parts which are then joined together (local quench). Specifically we focus on the transverse Ising chain and compute the time-dependence of the magnetization profile, m_l(t), and correlation functions at the critical point, in the ferromagnetically ordered phase and in the paramagnetic phase. At the critical point we find finite size scaling forms for the nonequilibrium magnetization and compare predictions of conformal field theory with our numerical results. In the ferromagnetic phase the magnetization profiles are well matched by our predictions from a quasi-classical calculation.

arXiv:1105.5317•Journal of Statistical Mechanics Theory and Experiment•Oct 24, 2011•36 citations
Abstract. We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method. ar X iv
We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method.
We present a quantitative semiclassical theory for the nonequilibrium dynamics of transverse Ising chains after quantum quenches, in particular, sudden changes of the transverse field strength. We obtain accurate predictions for the quench-dependent relaxation times and correlation lengths, and also about the recurrence times and quasiperiodicity of time-dependent correlations in finite systems with open or periodic boundary conditions. We compare the quantitative predictions of our semiclassical theory (local magnetization, equal-time bulk-bulk and surface-to-bulk correlations, and bulk autocorrelations) with the results from exact free-fermion calculations, and discuss the range of applicability of the semiclassical theory and possible generalizations and extensions.
We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large NNN limit of a O(NNN) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.
By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, , of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by , and in a finite sample of length L the average magnetization saturates at a size-dependent plateau here the two exponents satisfy the relation . Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until with and then starts to increase until it saturates to an asymptotic value , with . For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable . Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.
In this PhD thesis we investigate some properties of one-dimensional quantum systems, focusing on two important aspects of integrable models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will therefore be devoted to the study of the entanglement entropy in one-dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting theory with non perturbative solutions. We derive its bipartite Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap is analysed, both analytically and numerically. In particular it is worth mentioning that the numerical analysis of the entropies of the XYZ model presented in this dissertation has never been published in literature. In the second part of the thesis we study the dynamics of correlators after a quantum quench, preparing the system in a squeezed coherent initial state. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, the latter studied by means of the semi-classical theory, the former by a form-factor approach. Moreover in the last chapter we outline a general result about the dynamics of correlation functions of local observables after a quantum quench. In particular we show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model at long times (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations). For the Transverse Field Ising Chain this result means that its dynamics is described by a Generalized Gibbs Ensemble.
We study the quantum dynamics resulting from preparing a one-dimensional quantum system in the ground state of initially two decoupled parts which are then joined together (local quench). Specifically we focus on the transverse Ising chain and compute the time-dependence of the magnetization profile, m_l(t), and correlation functions at the critical point, in the ferromagnetically ordered phase and in the paramagnetic phase. At the critical point we find finite size scaling forms for the nonequilibrium magnetization and compare predictions of conformal field theory with our numerical results. In the ferromagnetic phase the magnetization profiles are well matched by our predictions from a quasi-classical calculation.