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arXiv:2511.01966 · Physical review. D/Physical review. D.

Entanglement asymmetry in gauge theories: chiral anomaly in the finite temperature massless Schwinger model

Adrien Florio, Sara Murciano

hep-thcond-mat.stat-mechhep-phnucl-thquant-phSubmitted Nov 3, 2025• Announced Nov 5, 2025• 3 citations
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Abstract

The entanglement asymmetry has emerged in recent years as a practical quantity to study phases of matter. We present the first study of entanglement asymmetry in gauge theories by considering the chiral anomaly of the analytically solvable massless Schwinger model at both zero and finite temperatures. At zero temperature, we find the asymmetry exhibits logarithmic growth with system size. At finite temperature, we show that it is parametrically more sensitive to chiral symmetry-breaking than the corresponding local order parameter: while the chiral condensate decays exponentially, the asymmetry decreases only logarithmically. This establishes the entanglement asymmetry as a promising tool to probe (finite-temperature) phase transitions in gauge theories.

Comments
9 pages, 4 figures

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The entanglement asymmetry has emerged in recent years as a practical quantity to study phases of matter. We present the first study of entanglement asymmetry in gauge theories by considering the chiral anomaly of the analytically solvable massless Schwinger model at both zero and finite temperatures. At zero temperature, we find the asymmetry exhibits logarithmic growth with system size. At finite temperature, we show that it is parametrically more sensitive to chiral symmetry-breaking than the corresponding local order parameter: while the chiral condensate decays exponentially, the asymmetry decreases only logarithmically. This establishes the entanglement asymmetry as a promising tool to probe (finite-temperature) phase transitions in gauge theories.
We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt βββ-VQE to evaluate thermal and quantum expectation values and study the phase diagram for massless Schwinger model along with the temperature and density. By compering the exact variational free energy, we find the variational algorithm work for T>0T>0T>0 and μ>0μ>0μ>0 for the Schwinger model. No significant volume dependence of the variational free energy is observed in μ/g∈[0,1.4]μ/g \in[0, 1.4]μ/g∈[0,1.4]. We calculate the chiral condensate and take the continuum extrapolation. As a result, we obtain qualitative picture of the phase diagram for massless Schwinger model.
Using matrix product operators, the Schwinger model is simulated in thermal equilibrium. The variational manifold of gauge-invariant matrix product operators is constructed to represent Gibbs states. As a first application, the chiral condensate in thermal equilibrium is computed, and agreement with earlier studies is found. Furthermore, as a new application, the Schwinger model is probed with a fractional charged static quark-antiquark pair separated infinitely far from each other. A critical temperature beyond which the string tension is exponentially suppressed is found and is in qualitative agreement with analytical studies in the strong coupling limit. Finally, the CTCTCT symmetry breaking is investigated, and our results strongly suggest that the symmetry is restored at any nonzero temperature.
The Schwinger model, or 1+1 dimensional QED, offers an interesting object of study, both at zero and non-zero temperature, because of its similarities to QCD.In this proceeding, we present the a full calculation of the temperature dependent chiral condensate of this model in the continuum limit using Matrix Product States (MPS).MPS methods, in general tensor networks, constitute a very promising technique for the non-perturbative study of Hamiltonian quantum systems.In the last few years, they have shown their suitability as ansatzes for ground states and low-lying excitations of lattice gauge theories.We show the feasibility of the approach also for finite temperature, both in the massless and in the massive case.
Entanglement spectrum ordering and flavor polarization in the two-flavor Schwinger model at vacuum angle θ=πθ= πθ=π
Entanglement spectra in gauge theories can encode both symmetry breaking and the organization of gauge sectors. In the two-flavor Schwinger model at vacuum angle θ=πθ=πθ=π, we find that the joint Schmidt distribution pQA,FAp_{Q_A,F_A}pQA​,FA​​, labeled by the subsystem gauge charge QAQ_AQA​ and flavor imbalance FAF_AFA​, reveals a cut-dependent gauge-sector hierarchy and a mass-induced flavor asymmetry: changing the staggered cut reorganizes the gauge-charge distribution pQAp_{Q_A}pQA​​, while mass imbalance breaks the FA↔−FAF_A\leftrightarrow-F_AFA​↔−FA​ symmetry of the conditional flavor distribution pFA∣QAp_{F_A|Q_A}pFA​∣QA​​. Defining the combined weight WF(q)=pq,+1+pq,−1W_F^{(q)}=p_{q,+1}+p_{q,-1}WF(q)​=pq,+1​+pq,−1​ and conditional polarization PF(q)=(pq,+1−pq,−1)/WF(q)\mathcal P_F^{(q)}=(p_{q,+1}-p_{q,-1})/W_F^{(q)}PF(q)​=(pq,+1​−pq,−1​)/WF(q)​, we find that changing the cut reverses the weight hierarchy, WF(−1)>WF(+1)W_F^{(-1)}>W_F^{(+1)}WF(−1)​>WF(+1)​ at unit-cell boundaries but WF(+1)>WF(−1)W_F^{(+1)}>W_F^{(-1)}WF(+1)​>WF(−1)​ at intra-cell cuts, while mass imbalance drives PF(q)\mathcal P_F^{(q)}PF(q)​ away from zero with a qqq-dependent cut response. Symmetry resolution therefore separates gauge-sector ordering, sector weight, and flavor polarization that are mixed in the globally ordered entanglement spectrum.
The Schwinger model, or 1+1 dimensional QED, offers an interesting object of study, both at zero and non-zero temperature, because of its similarities to QCD. In this proceeding, we present the a full calculation of the temperature dependent chiral condensate of this model in the continuum limit using Matrix Product States (MPS). MPS methods, in general tensor networks, constitute a very promising technique for the non-perturbative study of Hamiltonian quantum systems. In the last few years, they have shown their suitability as ansatzes for ground states and low-lying excita- tions of lattice gauge theories. We show the feasibility of the approach also for finite temperature, both in the massless and in the massive case.
Abstract Global symmetries of quantum many-body systems can be spontaneously broken. Whenever this mechanism happens, the ground state is degenerate and one encounters an ordered phase. In this study, our objective is to investigate this phenomenon by examining the entanglement asymmetry of a specific region. This quantity, which has recently been introduced in the context of U(1) symmetry breaking, is extended to encompass arbitrary finite groups G. We also establish a field theoretic framework in the replica theory using twist operators. We explicitly demonstrate our construction in the ordered phase of the Ising field theory in 1+1 dimensions, where a ℤ2 symmetry is spontaneously broken, and we employ a form factor bootstrap approach to characterise a family of composite twist fields. Analytical predictions are provided for the entanglement asymmetry of an interval in the Ising model as the length of the interval becomes large. We also propose a general conjecture relating the entanglement asymmetry and the number of degenerate vacua, expected to be valid for a large class of states, and we prove it explicitly in some cases.