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International Symposium on Lattice Field Theory (LATTICE)

Thermal evolution of the 1-flavour Schwinger model with using Matrix Product States

H. Saito, Mari Carmen Bañuls, Krzysztof Cichy, J. I. Cirac, Karl Jansen

Published Jul 15, 2016• 10 citations
Publisher

Abstract

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.

DOI
10.22323/1.251.0283

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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.
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.
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 nonzero 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.
We present our recent results for the tensor network (TN) approach to lattice gauge theories. TN methods provide an efficient approximation for quantum many-body states. We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model. In this study, we compute the chiral condensate at finite temperature. From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.
We present our recent results for the tensor network (TN) approach to lattice gauge theories.TN methods provide an efficient approximation for quantum many-body states.We employ TN for one dimensional systems, Matrix Product States, to investigate the 1-flavour Schwinger model.In this study, we compute the chiral condensate at finite temperature.From the continuum extrapolation, we obtain the chiral condensate in the high temperature region consistent with the analytical calculation by Sachs and Wipf.
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems.The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems.In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model.We deduced the ground state and lowest lying excitations.Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field.In this proceeding we continue our work on the Schwinger model.We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states.Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.