Quantum Domain Walls Induce Incommensurate Supersolid Phase on the Anisotropic Triangular Lattice

Abstract

We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both hopping and nearest-neighbor interaction strength. At half-filling the system can be tuned from decoupled one-dimensional chains to a two-dimensional solid phase with alternating density order by adjusting the anisotropic coupling. At intermediate anisotropy, however, frustration effects dominate and an incommensurate supersolid phase emerges, which is characterized by incommensurate density order as well as an anisotropic superfluid density. We demonstrate that this intermediate phase results from the proliferation of topological defects in the form of quantum bosonic domain walls. Accordingly, the structure factor has peaks at wave vectors, which are linearly related to the number of domain walls in a finite system in agreement with extensive quantum Monte Carlo simulations. We discuss possible connections with the supersolid behavior in the high-temperature superconducting striped phase. [42,43]. For hard-core bosons in optical lattices the hopping parameter plays the role of a ferromagnetic xy-coupling. In this case, nearest neighbor interacting bosons are realizable, for instance, with magnetic erbium atoms [48]. On the triangular lattice [49,50] they have been predicted to show supersolid behavior [12][13][14][15][16][17][18][19][20][21], which is characterized by two independent spontaneously broken symmetries -U(1) and translation -with corresponding superfluid and density order. For an anisotropic triangular lattice the commensurate supersolid phase is found to be unstable [26,27], and the solid order turns out to be incommensurate [41].Supersolid phases with two independently broken order parameters were first discussed for solid He [51,52] and were more recently shown to exist theoretically [12][13][14][15][16][17][18][19][20][21] and experimentally [53,54] in optical lattices for ultracold gases. Although high-temperature superconductors [55][56][57] are not often mentioned in this context, the coexistence of superconductivity and anti-ferromagnetic density order, so-called superstripes, are the defining characteristics of an incommensurate supersolid. Remarkably, the analogous physical phenomenon of incommensurate density order together with a finite superfluid density can be observed in a simple hard-core boson model. In the following we present a quantitative analytical model for this behavior in terms of topological defects in their simplest form, namely an increasing number of domain walls. Obviously the microscopic model of high-temperature superconductors is quite different, but the detailed understanding of the underlying mechanism via a spontaneous appearance of domain walls [55-57] is a helpful unifying feature of these many-body phenomena.In this paper we analyze the quantum phase diagram of hard-core bosons with anisotropic hopping t, t ′ ≥ 0 and nearest neighbor interactions V, V ′ ≥ 0 on a triangular latticê H =

Ground-state phase diagram of the frustrated spin- 12 two-leg honeycomb ladder

“…7 for the SD-Haldane transition. From the scaling of D s L we obtain the critical point J ⊥,c /J 1 ≃ −1.8980 (5), critical exponents β = 0.126 (2) and ν = 0.98 (2). These values coincide well with the critical indices of the 2D Ising universality class where β = 1/8 and ν = 1.…”

“…These values coincide well with the critical indices of the 2D Ising universality class where β = 1/8 and ν = 1. Following the same way introduced in the previous subsection, we get the central charge at the critical point J ⊥,c , c = 0.51 (2), which is another independent evidence of the 2D Ising universality class.…”

“…with H legs = α=1,2 L j=1 (J 1 S j,α · S j+1,α + J 2 S j,α · S j+2,α ) (2) where α = 1, 2 are the leg indices, and the interleg exchange on the odd rungs reads…”

“…Frustration due to competing interactions in quantum spin systems often gives rise to interesting and rich quantum phase diagrams. 1,2 The prototypical example of a spin-1/2 chain with frustrating next-nearestneighbor (NNN) interactions J 2 is known to undergo a Berezinskii-Kosteriz-Thouless (BKT) transition from a gapless Tomonaga-Luttinger liquid (TLL) phase to a gapped dimerized phase with spontaneously broken translational symmetry [3][4][5][6][7] at J 2,c ≃ 0.241167J 1 where J 1 is the nearest neighbor (NN) interaction along the chain. At the Majumdar-Ghosh point 8,9 J 2 = J 1 /2 the ground state is known exactly and for J 2 > J 1 /2 incommensurate spiral spin-spin correlations emerge.…”

“…FSS analysis of the staggered dimerization order parameter D s L for J2 = 0.7J1 as a function of J ⊥ for different length L = 96 (∆), 128 ( ), 160 ( ) and 192 ( ). The best fitting suggests J ⊥,c = −1.8980(5) and critical exponents β = 0.126(2) and ν = 0.98(2).…”