Quantum Phase Transition in Lattice Model of Unconventional Superconductors

TL;DR

This paper introduces a lattice gauge model for unconventional d-wave superconductors to study quantum phase transitions at zero temperature, revealing multiple second-order phase transitions and comparing results with analytical models.

Contribution

The paper develops a noncompact U(1) lattice-gauge-Higgs model for d-wave superconductors derived from microscopic Hamiltonian, and investigates its phase structure via Monte Carlo simulations.

Findings

Identified a second-order phase transition from normal to superconducting phase.

Discovered an additional second-order phase transition within the superconducting phase.

Compared magnetic penetration depth behavior with previous analytical XY model results.

Abstract

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature ($T$). Finite-$T$ counterpart of the present model was proposed previously with which SC phase transition at finite $T$ was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.