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arXiv:2205.08860

Schwinger model at finite temperature and density with beta VQE

Akio Tomiya

Published May 18, 2022• 3 citations
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Abstract

We investigate a quantum gauge theory at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt $β$-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 $T>0$ and $μ>0$ for the Schwinger model. No significant volume dependence of the variational free energy is observed in $μ/g \in[0, 1.4]$. 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.

DOI
10.48550/arxiv.2205.08860

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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.
We study the Schwinger model at finite temperature and density using a variational algorithm for near-term quantum devices. We adapt β\betaβ-VQE, a classical-quantum hybrid algorithm with a neural network, to evaluate thermal and quantum expectation values and study the phase diagram for the massless Schwinger model along with the temperature and density. By comparing the exact variational free energy, we find that the variational algorithm works for the Schwinger model for T>0T>0T>0 and μ\muμ>0. As a result, we obtain a qualitative picture of the phase diagram for the massless Schwinger model.
Confinement of quarks due to the strong interaction and the deconfinement at high temperatures and high densities are a basic paradigm for understanding the nuclear matter. Their simulation, however, is very challenging for classical computers due to the sign problem of solving equilibrium states of finite-temperature quantum chromodynamical systems at finite density. In this paper, we propose a variational approach, using the lattice Schwinger model, to simulate the confinement or deconfinement by investigating the string tension. We adopt an ansatz that the string tension can be evaluated without referring to quantum protocols for measuring the entropy in the free energy. Results of numeral simulation show that the string tension decreases both along the increasing of the temperature and the chemical potential, which can be an analog of the phase diagram of QCD. Through numerical simulations on the classical computer, we demonstrate the potential of exploiting near-term quantum computers for investigating the phase diagram of finite-temperature and finite-density nuclear matters.
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 study the Schwinger model at finite-temperature regime using a quantum-classical hybrid algorithm. The preparation of thermal state on quantum circuit presents significant challenges. To address this, we adopt the Thermal Pure Quantum (TPQ) state approach and apply the Quantum Imaginary Time Evolution (QITE) algorithm to implement the necessary imaginary time evolution. We first compute the chiral condensate in the massless Schwinger model, verifying its consistency with the analytical solution. We then simulate the massive Schwinger model with non-zero topological θ\thetaθ-term to investigate the temperature and θ\thetaθ-dependence of the chiral condensate. Our method works well even at non-zero θ\thetaθ regime, while the conventional lattice Monte Carlo method suffers from the sign problem in this system.
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.
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.