Chiral condensate in the Schwinger model with Matrix Product Operators

Abstract

Tensor network (TN) methods, in particular the Matrix Product States (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the non-zero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.

24 pages, 9 figures

References in corpus (15)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• DMRG and periodic boundary conditions: a quantum information perspective
• Operator space entanglement entropy in transverse Ising chain
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Quantum simulation of the Schwinger model: A study of feasibility
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Lattice Gauge Tensor Networks
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Lattice Hamiltonian approach to the massless Schwinger model: precise extraction of the mass gap
• The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States
• Finite Temperature Schwinger Model

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