Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange

TL;DR

This paper provides evidence for new quasi-one-dimensional phases related to the d-wave Bose liquid, including a gapless Bose metal and a gapless Mott insulator, studied via models of bosons on multi-leg ladders with ring exchange.

Contribution

It introduces two novel phases on multi-leg ladders with ring exchange, supporting the stability of the d-wave Bose liquid in two dimensions.

Findings

Identified a gapless Bose metal with five gapless modes on four-leg ladders.

Discovered an incompressible gapless Mott insulator with two modes on three-leg ladders.

Used variational wave functions and DMRG to analyze phase properties.

Abstract

We establish compelling evidence for the existence of new quasi-one-dimensional descendants of the d-wave Bose liquid (DBL), an exotic two-dimensional quantum phase of uncondensed itinerant bosons characterized by surfaces of gapless excitations in momentum space [O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B {\bf 75}, 235116 (2007)]. In particular, motivated by a strong-coupling analysis of the gauge theory for the DBL, we study a model of hard-core bosons moving on the $N$-leg square ladder with frustrating four-site ring exchange. Here, we focus on four- and three-leg systems where we have identified two novel phases: a compressible gapless Bose metal on the four-leg ladder and an incompressible gapless Mott insulator on the three-leg ladder. The former is conducting along the ladder and has five gapless modes, one more than the number of legs. This represents a significant step forward in establishing the potential stability of the DBL in two dimensions. The latter, on the other hand, is a fundamentally quasi-one-dimensional phase that is insulating along the ladder but has two gapless modes and incommensurate power law transverse density-density correlations. In both cases, we can understand the nature of the phase using slave-particle-inspired variational wave functions consisting of a product of two distinct Slater determinants, the properties of which compare impressively well to a density matrix renormalization group solution of the model Hamiltonian. Stability arguments are made in favor of both quantum phases by accessing the universal low-energy physics with a bosonization analysis of the appropriate quasi-1D gauge theory. We will briefly discuss the potential relevance of these findings to high-temperature superconductors, cold atomic gases, and frustrated quantum magnets.