Supersolid-Superfluid phase separation in the extended Bose-Hubbard model

TL;DR

This paper investigates a phase-separated state in the extended Bose-Hubbard model, revealing a coexistence of supersolid and superfluid phases with distinct spatial and entanglement properties, analyzed through advanced numerical methods.

Contribution

It demonstrates that the new phase is a phase-separated state generated by mechanical instability, characterized by unique entanglement and correlation patterns, and models its low-energy excitations as a Luttinger liquid.

Findings

Phase separation into supersolid and superfluid observed.

Elementary excitations identified as phonons with c=1.

Velocity of sound matches dynamical simulations.

Abstract

Recent studies have suggested a new phase in the extended Bose-Hubbard model in one dimension at integer filling [1,2]. In this work, we show that this new phase is phase-separated into a supersolid and superfluid part, generated by mechanical instability. Numerical simulations are performed by means of the density matrix renormalization group algorithm in terms of matrix product states. In the phase-separated phase and the adjacent homogeneous superfluid and supersolid phases, we find peculiar spatial patterns in the entanglement spectrum and string-order correlation functions and show that they survive in the thermodynamic limit. In particular, we demonstrate that the elementary excitations of the homogeneous superfluid with enhanced periodic modulations are phonons, find the central charge to be $c=1$, and show that the velocity of sound, extracted from the intrinsic level splitting for finite systems, matches with the propagation velocity of local excitations in dynamical simulations. This suggests that the low-energy spectrum of the phase under investigation is effectively captured by a spinless Luttinger liquid, for which we find consistent results between the Luttinger parameter obtained from the linear dependence of the structure factor and the algebraic decay of the one-body density matrix.