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

arXiv:1309.7915

Effects of spontaneous symmetry break in the origin of non-analytic behavior of entanglement at quantum phase transitions

L. Justino, Thiago Rodrigues de Oliveira

Published Sep 30, 2013• 0 citations
arXivHTMLPDF

Abstract

We present an example where Spontaneous Symmetry Breaking may effect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of the non-analyticity. In particular, in the XXZ model, we study the non analyticities in the concurrence between two spins, which was claimed to be accidental, since it had its origin in the optimization involved in the concurrence definition. We show that when one takes in account the effect of the Spontaneous Symmetry Breaking, even tough the values of the entanglement measure does not change, the origin the the non-analytical behavior changes: it is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the Spontaneous Symmetry Breaking not noticed before. However the non-analytical behavior still suggests a second order quantum phase transition and not the first order that occurs and we explain why. We also show that the value of entanglement between one site and the rest of the chain does change when taking into account the Spontaneous Symmetry Breaking.

DOI
10.48550/arxiv.1309.7915

Related papers

Effects of Spontaneous Symmetry Break in the Origin of Non-analytic Behavior of Entanglement at Quantum Phase Transitions

L. J. Pereira, Thiago Rodrigues de Oliveira

We present an example where spontaneous symmetry breaking may affect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of its non-analyticity. In particular, in the XXZ model, we study the non-analyticities in the concurrence between two spins, which was claimed to be accidental since it had its origin in the optimization involved in the concurrence definition. We show that when one takes into account the effect of the spontaneous symmetry breaking, even though the values of the entanglement measure does not change, the origin of the non-analytical behavior changes. The non-analytical behavior is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the spontaneous symmetry breaking not observed before. We also show that the value of entanglement between one site and the rest of the chain changes after taking into account the spontaneous symmetry breaking.

Frontiers in Physics•Dec 21, 2016•4 citations

Entanglement and spontaneous symmetry breaking in quantum spin models

Olav F. Syljuåsen

It is shown that spontaneous symmetry breaking does not modify the ground-state entanglement of two spins, as defined by the concurrence, in the XXZ chain and the transverse field Ising chain. Correlation function inequalities, valid in any dimensions for these models, are presented outlining the regimes where entanglement is unaffected by spontaneous symmetry breaking.

arXiv:quant-ph/0307087•Physical Review A•Dec 2, 2003•129 citations

Symmetry-breaking effects upon bipartite and multipartite entanglement in the XY model

Thiago Rodrigues de Oliveira, Gustavo Rigolin, M. C. de Oliveira +1 more

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional $XY$ model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long-range correlations in quantum phase transitions.

arXiv:0709.1956•Physical Review A•Mar 14, 2008•42 citations

Observing quantum phase transitions at non-zero temperature: non-analytic behavior of order-parameter correlation times

István Csépányi, Giuseppe Del Vecchio Del Vecchio, Benjamin Doyon +1 more

Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.

arXiv:2602.00794•Jan 31, 2026•0 citations

Anomalous Spontaneous Symmetry Breaking in non-Hermitian Systems with Biorthogonal Z2-symmetry

Meng-Lei Yang, Heng Wang, Cui-Xian Guo +3 more

Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.

arXiv:2006.10278•Jun 18, 2020•5 citations

Enhancement of Pairwise Entanglement via Z2 Symmetry Breaking

Andreas Osterloh, Guillaume Palacios, Simone Montangero

We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.

arXiv:cond-mat/0608244•Physical Review Letters•Dec 18, 2006•38 citations
We present an example where Spontaneous Symmetry Breaking may effect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of the non-analyticity. In particular, in the XXZ model, we study the non analyticities in the concurrence between two spins, which was claimed to be accidental, since it had its origin in the optimization involved in the concurrence definition. We show that when one takes in account the effect of the Spontaneous Symmetry Breaking, even tough the values of the entanglement measure does not change, the origin the the non-analytical behavior changes: it is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the Spontaneous Symmetry Breaking not noticed before. However the non-analytical behavior still suggests a second order quantum phase transition and not the first order that occurs and we explain why. We also show that the value of entanglement between one site and the rest of the chain does change when taking into account the Spontaneous Symmetry Breaking.
We present an example where spontaneous symmetry breaking may affect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of its non-analyticity. In particular, in the XXZ model, we study the non-analyticities in the concurrence between two spins, which was claimed to be accidental since it had its origin in the optimization involved in the concurrence definition. We show that when one takes into account the effect of the spontaneous symmetry breaking, even though the values of the entanglement measure does not change, the origin of the non-analytical behavior changes. The non-analytical behavior is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the spontaneous symmetry breaking not observed before. We also show that the value of entanglement between one site and the rest of the chain changes after taking into account the spontaneous symmetry breaking.
We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XYXYXY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long-range correlations in quantum phase transitions.
Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.
Landau's spontaneous symmetry breaking theory is a fundamental theory that describes the collective behaviors in many-body systems. It was well known that for usual spontaneous symmetry breaking in Hermitian systems, the order-disorder phase transition with gap closing and spontaneous symmetry breaking occur at the same critical point. In this paper, we generalized the Landau's spontaneous symmetry breaking theory to the cases in non-Hermitian (NH) many-body systems with biorthogonal Z2 symmetry and tried to discover certain universal features. We were surprised to find that the effect of the NH terms splits the spontaneous biorthogonal Z2 symmetry breaking from a (biorthogonal) order-disorder phase transition with gap closing. The sudden change of similarity for two degenerate ground states indicates a new type of quantum phase transition without gap closing accompanied by spontaneous biorthogonal Z2 symmetry breaking. We will take the NH transverse Ising model as an example to investigate the anomalous spontaneous symmetry breaking. The numerical results were consistent with the theoretical predictions.
We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.