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arXiv:0707.3930 · Physical Review A

Superfluid-insulator and roughening transitions in domain walls

Şebnem Güneş Söyler, Barbara Capogrosso-Sansone, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Oct 29, 2007• 9 citations
arXivHTMLPDF

Abstract

We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-$1∕2$ quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional $\mathrm{U}(1)$ universality class and the interface remains smooth. Similar phenomena are expected for domain walls in quantum antiferromagnets.

DOI
10.1103/physreva.76.043628

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We have performed quantum Monte Carlo simulations to investigate the superfluid behavior of one- and two-dimensional interfaces separating checkerboard solid domains. The system is described by the hard-core Bose-Hubbard Hamiltonian with nearest-neighbor interaction. In accordance with Burovski et al. [Phys. Rev. Lett. 94, 165301 (2005)] we find that (i) the interface remains superfluid in a wide range of interaction strength before it undergoes a superfluid-insulator transition; (ii) in one dimension, the transition is of the Kosterlitz-Thouless type and is accompanied by the roughening transition, driven by proliferation of charge-1∕21∕21∕2 quasiparticles; (iii) in two dimensions, the transition belongs to the three-dimensional U(1)\mathrm{U}(1)U(1) universality class and the interface remains smooth. Similar phenomena are expected for domain walls in quantum antiferromagnets.
We study the superfluid-insulator transition in Bose-Hubbard models in one-, two-, and three-dimensional cubic lattices by means of a recently proposed variational wave function. In one dimension, the variational results agree with the expected Berezinskii-Kosterlitz-Thouless scenario of the interaction-driven Mott transition. In two and three dimensions, we find evidence that, across the transition, most of the spectral weight is concentrated at high energies, suggestive of preformed Mott-Hubbard sidebands. This result is compatible with the experimental data by Stoferle et al. [Phys. Rev. Lett. 92, 130403 (2004)].
We study hard-core bosons on the checkerboard lattice with nearest-neighbor unfrustrated hopping ttt and ``tetrahedral'' plaquette charging energy UUU. Analytical arguments and quantum Monte Carlo simulations lead us to the conclusion that the system undergoes a zero temperature (T)(T)(T) quantum phase transition from a superfluid phase at small U∕tU∕tU∕t to a large U∕tU∕tU∕t Mott insulator phase with $\ensuremath{\rho}=1∕4$ for a range of values of the chemical potential $\ensuremath{\mu}$. Further, the quarter-filled insulator breaks lattice translation symmetry in a characteristic fourfold ordering pattern and occupies a lobe of finite extent in the $\ensuremath{\mu}\text{\ensuremath{-}}U∕t$ phase diagram. A quantum Monte Carlo study slightly away from the tip of the lobe provides evidence for a direct weakly first-order superfluid insulator transition away from the tip of the lobe. While analytical arguments lead us to conclude that the transition at the tip of the lobe belongs to a different Landau-forbidden second-order universality class, an extrapolation of our numerical results suggests that the size of the first-order jump does not go to zero even at the tip of the lobe.
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.
We use two quantum Monte Carlo algorithms to map out the phase diagram of the two-dimensional hardcore boson Hubbard model with near (V1){(V}_{1})(V1​) and next near (V2){(V}_{2})(V2​) neighbor repulsion. At half filling we find three phases: superfluid (SF), checkerboard solid, and striped solid depending on the relative values of V1,V2,{V}_{1}{,V}_{2},V1​,V2​, and the kinetic energy. Doping away from half filling, the checkerboard solid undergoes phase separation: The superfluid and solid phases coexist but not as a single thermodynamic phase. As a function of doping, the transition from the checkerboard solid is therefore first order. In contrast, doping the striped solid away from half filling instead produces a striped supersolid phase: coexistence of density order with superfluidity as a single phase. One surprising result is that the entire line of transitions between the SF and checkerboard solid phases at half filling appears to exhibit dynamical O(3)O(3)O(3) symmetry restoration. The transitions appear to be in the same universality class as the special Heisenberg point even though this symmetry is explicitly broken by the V2{V}_{2}V2​ interaction.
We study the superfluid-insulator transition in a one-dimensional system of interacting bosons, modeled as a disordered Josephson array, using a strong-randomness real-space renormalization-group technique. Unlike perturbative methods, this approach does not suffer from run-away flows and allows us to study the complete phase diagram. We show that the superfluid-insulator transition is always Kosterlitz-Thouless like in the way that length and time scales diverge at the critical point. Interestingly however, we find that the transition at strong disorder occurs at a nonuniversal value of the Luttinger parameter, which depends on the disorder strength. This result places the transition in a universality class different from the weak disorder transition first analyzed by Giamarchi and Schulz [Europhys. Lett. 3, 1287 (1987)]. While the details of the disorder potential are unimportant at the critical point, the type of disorder does influence the properties of the insulating phases. We find three classes of insulators which arise for different classes of disorder potential. For disorder only in the charging energies and Josephson coupling constants, at integer filling we find an incompressible but gapless Mott-glass phase. If both integer and half-integer filling factors are allowed then the corresponding phase is a random-singlet insulator, which has a divergent compressibility. Finally in a generic disorder potential the insulator is a Bose glass with a finite compressibility.