Abstract
Employing matrix product states as an ansatz, we study the non-thermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with non-zero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behaviour, and serve as an important ingredient for controlling the continuum extrapolation of the model.
Highlights
Many quantum field theories of interest cannot be studied with perturbative methods
This led to spectacular successes, in the most important theory studied with lattice methods, i.e., quantum chromodynamics (QCD)
In addition to the soliton solutions that can be related to fermions in the Thirring model [91], the sine-Gordon theory exhibits interesting scaling behavior and phase structure, which can be understood from studying its renormalization group (RG) equations [92,93,94]. Since this aspect of the theory is important for the current work, here we describe the scenario in slightly more detail
Summary
Many quantum field theories of interest cannot be studied with perturbative methods. The path integral corresponding to a discretized system is finite dimensional, but usually this dimension is very large, implying no alternative to Monte Carlo sampling. If such sampling is possible, the lattice provides an unambiguous way of reaching results with an arbitrary precision, with controllable total error. This led to spectacular successes, in the most important theory studied with lattice methods, i.e., QCD. Several aspects of QCD were addressed with large-scale simulations, including hadron
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