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Journal of the Korean Physical Society

A signature of the quantum phase transition in a hard-core boson model in one dimension

Gi Wook Shin, Ji-Woo Lee

Published Feb 1, 2012• 1 citation
Publisher

Abstract

We study quantum phase transitions in a hard-core boson model with nearest-neighbor repulsions in one dimension. As we change the repulsive energy, V , between bosons occupying nearest neighbors, the model exhibits a quantum phase transition from a superfluid (SF) to a charge-density-wave (CDW)-type solid phase at half-filling. By using an exact diagonalization method with a modified Lanczos method, we calculate the ground-state energies up to a precision of O (10 −7 ). From the ground-state energies, we obtain the number of dimers by taking numerical derivatives of the groundstate energies. Because the dissolution of the dimers occurs because of the repulsive energy, V , we find a signature of the quantum phase transition from the behaviors of the correlation energy and those of the number of dimers as a function of V .

DOI
10.3938/jkps.60.633

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We study quantum phase transitions in a hard-core boson model with nearest-neighbor repulsions in one dimension. As we change the repulsive energy, V , between bosons occupying nearest neighbors, the model exhibits a quantum phase transition from a superfluid (SF) to a charge-density-wave (CDW)-type solid phase at half-filling. By using an exact diagonalization method with a modified Lanczos method, we calculate the ground-state energies up to a precision of O (10 −7 ). From the ground-state energies, we obtain the number of dimers by taking numerical derivatives of the groundstate energies. Because the dissolution of the dimers occurs because of the repulsive energy, V , we find a signature of the quantum phase transition from the behaviors of the correlation energy and those of the number of dimers as a function of V .
We study a model for interacting spinless bosons in one dimension. The bosons are under a hard-core condition, which does not allow two or more bosons in the same site. However, nearestneighbor interactions between bosons ( V ) and hoppings to the nearest empty site ( t ) are allowed. As V increases from a large negative value, the system undergoes a quantum phase transition from a phase-separation (PS) phase to a superfluid (SF) phase because the hopping term overcomes the attractive energy. When V becomes positive and is increased more, the superfluid phase becomes a charge-density-wave (CDW) phase because the repulsive energy blocks the movements of bosons. Via exact diagonalizations, we calculated the ground-state energies, the correlation energies, and the kinetic energies to obtain signatures of the quantum phase transitions. We adopted a fast stateseeking algorithm that enabled us to calculate the ground states and the ground-state energies up to L = 32 more efficiently. Some results are compared with those of quantum Monte Carlo simulations by using stochastic series expansion for the Heisenberg point, and the momentum distribution functions for the three phases are discussed.
We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model.
We investigate the momentum distribution associated with quantum phase transitions between a superfluid and a charge-density-wave state in the one-dimensional hard-core extended boson Hubbard model at half filling by using the Lanczos exact diagonalization method. The momentum distribution shows distinct features in different regions. At the Heisenberg point, it shows a universal behavior. In the superfluid phase, the Luttinger-liquid parameters are easily obtained from the finite-size scaling behaviors of the zero-momentum occupancy. Also the signature of a charge-density wave can be identified in the insulating phase.
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. Away from half-filling, we show that the presence of next-nearest-neighbor hopping in the effective Hamiltonian leads to a superfluid-to-supersolid transition at intermediate boson-phonon (b-p) couplings, while at strong-couplings the system phase separates. However, at half-filling and at a critical b-p coupling (as in the xxz-model), the system undergoes a superfluid-to-charge-density-wave transition without any signature of supersolidity. Our analyses is based on extensive calculations of the structure factor, the superfluid fraction, the Bose-Einstein condensate fraction, and the system energy at various fillings. We present a phase diagram for this system and compare it to that of the xxz-model. We also demonstrate explicitly that the next-nearest-neighbor hopping (in the absence of nearest-neighbor hopping) in the effective Hamiltonian leads only to a single transition, i.e., a first-order superfluid-to-supersolid transition.
Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions.
We study the ground-state properties of repulsively interacting bosons on the honeycomb lattice using large-scale quantum Monte Carlo simulations. In the hard-core limit, the half-filled system develops long-ranged diagonal order for sufficiently strong nearest-neighbor repulsion. This staggered solid melts at a first-order quantum phase transition into the superfluid phase, without the presence of any intermediate supersolid phase. Within the superfluid phase, both the superfluid density and the compressibility exhibit local minima near the particle (hole) density of one quarter, while the density and the condensate fraction show inflection points in this region. Relaxing the hard-core constraint, supersolid phases emerge for soft-core bosons. The suppression of the superfluid density is found to persist for sufficiently large, finite on-site repulsion.