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Physical review. B, Condensed matter

Supersolid phases in underdamped Josephson arrays: Quantum Monte Carlo simulations

Eric Roddick, D. Stroud

Published Apr 1, 1995• 25 citations
Publisher

Abstract

We carry out a quantum Monte Carlo study of Josephson arrays at temperature T=0 in the presence of an offset voltage between array and substrate. With diagonal and nearest-neighbor charge coupling, we find two types of insulating lobes with different types of charge order, and two types of superconducting regions. One is a supersolid with coexisting long-range phase coherence and checkerboard charge order. The supersolid phase is robust at half-filling. With next-nearest-neighbor coupling, there are two types of supersolid phase, one with checkerboard and one with striped charge order. Our phase diagram agrees with mean-field theory and with quantum Monte Carlo results of van Otterlo et al. in comparable regions of parameter space, but differs in detail from that of a Bose-Hubbard model with nearest-neighbor charging energies.

DOI
10.1103/physrevb.51.8672

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We carry out a quantum Monte Carlo study of Josephson arrays at temperature T=0 in the presence of an offset voltage between array and substrate. With diagonal and nearest-neighbor charge coupling, we find two types of insulating lobes with different types of charge order, and two types of superconducting regions. One is a supersolid with coexisting long-range phase coherence and checkerboard charge order. The supersolid phase is robust at half-filling. With next-nearest-neighbor coupling, there are two types of supersolid phase, one with checkerboard and one with striped charge order. Our phase diagram agrees with mean-field theory and with quantum Monte Carlo results of van Otterlo et al. in comparable regions of parameter space, but differs in detail from that of a Bose-Hubbard model with nearest-neighbor charging energies.
We use quantum Monte Carlo simulations to determine the ground state phase diagram of the Bose-Hubbard Hamiltonian with long-range repulsive interactions. At half filling one finds superfluidity and insulating solid phases. Depending on the relative sizes of near-neighbor and next-near-neighbor interactions, this solid follows either a checkerboard or a striped pattern. In neither case is there a coexistence with superfluidity. However, at incommensurate densities ``supersolid'' phases appear with simultaneous diagonal and off-diagonal long-range order.
Understanding the microscopic mechanism of coexisting long-range orders (such as lattice supersolidity) in strongly correlated systems is a subject of immense interest. We study the possible manifestations of long-range orders, including lattice-supersolid phases with differently broken symmetry, in a two-dimensional square lattice system of hard-core bosons (HCBs) coupled to archetypal cooperative/coherent normal-mode distortions such as those in perovskites. At strong HCB-phonon coupling, using a duality transformation to map the strong-coupling problem to a weak-coupling one, we obtain an effective Hamiltonian involving nearest-neighbor, next-nearest-neighbor, and next-to-next-nearest-neighbor hoppings and repulsions. Using stochastic series expansion quantum Monte Carlo, we construct the phase diagram of the system. As coupling strength is increased, we find that the system undergoes a first-order quantum phase transition from a superfluid to a checkerboard solid at half-filling and from a superfluid to a diagonal striped solid [with crystalline ordering wave vector $\stackrel{P\vec}{Q}=(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ or $(2\ensuremath{\pi}/3,4\ensuremath{\pi}/3)]$ at one-third filling without showing any evidence of supersolidity. On tuning the system away from these commensurate fillings, checkerboard supersolid is generated near half-filling whereas a rare diagonal striped supersolid is realized near one-third filling. Interestingly, there is an asymmetry in the extent of supersolidity about one-third filling. Within our framework, we also provide an explanation for the observed checkerboard and stripe formations in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{NiO}}_{4}$ at x=1/2x=1/2x=1/2 and x=1/3x=1/3x=1/3.
We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.
The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and ``star'' diagonal ordering is found for filling $\ensuremath{\rho}<0.25$. At filling $\ensuremath{\rho}>0.25$, a supersolid phase exists between the star and the stripe crystal at $\ensuremath{\rho}=0.5$. No supersolid phase occurs for $\ensuremath{\rho}>0.25$ if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.
We study the phase diagram at finite temperature of Josephson junction arrays with capacitive disorder (i.e., random offset charges and/or random charging energies): in the limit of large particle numbers per junction, this is a remarkable physical realization of the disordered boson Hubbard model. By using a mean-field approximation, we compute the average free energy and the equation for the phase boundary line between the insulating and superconducting phases. We find that the Mott-insulating lobe structure disappears for large variance $(\ensuremath{\sigma}\ensuremath{\gtrsim}e)$ of the offset charges probability distribution. Further, with nearest-neighbor interactions, the insulating lobe around q=eq=eq=e is destroyed even for small values of $\ensuremath{\sigma}.$ In the case of random charging energies, until the variance of the distribution reaches some critical value the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.
We numerically study the ground state phase diagram of the two-dimensional hard-core Bose-Hubbard model with nearest-(V(1)) and next-nearest-neighbour (V(2)) repulsions. In particular, we focus on the quarter-filled phases where one supersolid and two solid phases are observed. Using both canonical and grand canonical quantum Monte Carlo (QMC) methods and a mean-field calculation, we provide evidence for the existence of a commensurate supersolid. Despite the two possible diagonal long-range orderings for the solid phase, only one kind of supersolid phase is found to be energetically stable. The competition between the two solid phases manifests itself as a first-order phase transition around 2V(2) ∼ V(1). The change of order parameters as a function of the chemical potential is also presented.