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arXiv:1602.03687 · Physical review. B./Physical review. B

Drude weight in hard-core boson systems: Possibility of a finite-temperature ideal conductor

Gourab Majumder, Arti Garg

Published Oct 12, 2016• 1 citation
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Abstract

We calculate the Drude weight in the superfluid (SF) and supersolid (SS) phases of the hard-core boson (HCB) model on a square lattice using stochastic series expansion (SSE). We demonstrate from our numerical calculations that the normal phase of HCBs in two dimensions can be an ideal conductor with dissipationless transport. In two dimensions, when the ground state is a SF, the superfluid stiffness drops to zero with a Kosterlitz-Thouless type transition at ${T}_{\mathrm{KT}}$. The Drude weight, though is equal to the stiffness below ${T}_{\mathrm{KT}}$, surprisingly, stays finite even for a range of temperatures above ${T}_{\mathrm{KT}}$ indicating the nondissipative transport in the normal state of this system. In contrast to this, in a three-dimensional SF phase, where the superfluid stiffness goes to zero continuously via a second-order phase transition at ${T}_{c}$, the Drude weight goes to zero at ${T}_{c}$, as expected. We also calculated the Drude weight in a two-dimensional SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via a Kosterlitz-Thouless transition at ${T}_{\mathrm{KT}}$ and the transition temperature for the CDW order is larger than ${T}_{\mathrm{KT}}$. In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, the system behaves like an ideal conductor for a range of temperatures above ${T}_{\mathrm{KT}}$ along the lattice direction parallel to the stripes, while along the direction perpendicular to the stripes it behaves like an insulator for all $T>{T}_{\mathrm{KT}}$. In contrast to this, in the star-SS phase, the Drude weight along both lattice directions goes to zero along with the superfluid stiffness and for $T>{T}_{\mathrm{KT}}$ we have the finite temperature phase of a CDW insulator.

DOI
10.1103/physrevb.94.134508

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Abstract In this work, we theoretically study hard-core bosons on a two-dimensional square optical superlattice at T = 0. First of all, we present the mean field phase diagram of this model in terms of the chemical potential μ and the alternating potential strength Δ. Besides a superfluid (SF) phase at Δ = 0 and a charge density wave (CDW) phase in the large Δ at half filling, we demonstrate that a supersolid (SS) phase emerges in the moderate Δ. Then, we focus on the μ = 0, e.g., half filling case, using large-S semiclassical spin-wave approximation to study the SS to CDW quantum phase transition. In particular, we calculate the ground-state energy and the superfluid density at the level of 1/S correction. We then compare the spin-wave results with the large scale quantum Monte Carlo (QMC) simulations using the cluster stochastic series expansion (CSSE) algorithm, and find that while the spin wave method is intuitive with clear physical pictures, the quantum critical point is quite different from that of numerical results which is believed to be accurate. We suggest that as simple as it is, this model still exhibits strong quantum fluctuations near the quantum critical point beyond the power of semiclassical spin-wave approach.
We apply well-established finite-temperature quantum Monte Carlo techniques to one-dimensional Bose systems with soft- and hard-core constraints, as well as to spinless fermion systems. We give clear and robust numerical evidence that, as expected, no superfluid density for bosons or Meissner fraction for fermions is possible at any nonzero temperature in one-dimensional interacting Bose or Fermi lattice models, whereas a finite Drude weight is generally observed in gapless systems, in partial disagreement with previous expectations.
The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.