Excitation spectrum of a two-dimensional long-range Bose liquid with supersymmetry

Abstract

We have studied excitation spectrum of the specfic 2D model of strongly interacting Bose particles via mapping of the many-body Schrodinger equation in imaginary time to the classical stochastic dynamics. In a broad range of coupling strength α a roton-like spectrum is found, with the roton gap being extremely small in natural units. A single quantum phase transition between strongly correlated supefluid and quantum Berezinsky crystal is found.Usually the system of Bose particles at zero temperature exists in one of two possible ground-states: superfluid (SF) or crystalline (CR). More exotic option is a "supersolid" ground state suggested long ago [1], which attracted a lot of attention recently [2]; this is a state which is expected to possess both superfluid and crystalline order simultaneously. Another direction of the search for unusual quantum ground states is related with a search for a "Bose-metal", that is, a bosonic analog of a Fermi-liquid, see for example [3,4]. Such a state would possess neither superfluid no crystalline order. Suggestion for the search of such a strange quantum state was made 20 years ago in Ref. [5], in relation with classical thermodynamics of 3D vortex liquid in high-temperature superconductors. This idea was further developed in Ref. [6] where two different models of strongly interacting Bose-liquid were considered (note that Refs. [5,6] refer to continuous 2D Bose-liquids without any lattice, whereas Refs. [3,4] consider lattice models). The arguments were given in Ref. [6] in favor of existence of a new unusual ground-state which is still liquid, but is not superfluid. One of these models refers to 2D bosons interacting with a 2D dynamic U (1) gauge field, with an effective coupling constant ∼ 1. The second model (KKLZ, Ref. [7]) is purely static, it has a remarkable feature that its exact ground-state wavefunction is represented in a simple Jastrow form.It was shown later in Ref.[8] that KKLZ model obeys nonrelativistic supersymmetry which allows to obtain a number of interesting results analytically. The KKLZ model contains a coupling constant α such that small values α ≤ 3 definitely lead to a gapful superfluid state, whereas at very large α ≥ 35 a kind of a "Berezinsky crystal" with power-law decay of positional correlations is stabilized, according to Ref. [9]. An issue was raised in Ref.[8] about possible existence of a third, intermediate, ground-state of the "normal liquid" type, which could exist in some part of the broad range 3 ≤ α ≤ 35. Supersymmetry of KKLZ model makes it also possible to compute time-dependent quantum correlation functions via classical Langevin dynamics (the relation between supersymmetry and Langevin dynamics was discussed, in particular, in Ref.[10]). Similar approach was proposed by C.Henley [11] for the lattice quantum systems and used efficiently in Ref.[12] to explore excitation spectrum of quantum dimer models on square and triangular lattices at the Rokhsar-Kivelson point [13]. More recently, the same lines of ideas were developed in Ref...

The Inverse-Square Interaction Phase Diagram: Unitarity in the Bosonic Ground State

“…Both the wave function and energy can be explicitly written as a function of the interaction parameter both in homogeneous and trapped geometries [49][50][51][52]. It was observed that a similar construction of the ground state wave function in two dimensions leads to equivalent statistical averages as for a system of classical charges, while the quantum Hamiltonian in addition possesses three-body interaction terms [53][54][55][56].…”