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arXiv:0812.1987

Quantum phase transition in Bose-Holstein model in two dimensions

Sanjoy Datta, Sudhakar Yarlagadda

Published Dec 10, 2008• 1 citation
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Abstract

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.

DOI
10.48550/arxiv.0812.1987

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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.
We derive an effective d-dimensional Hamiltonian for a system of hard-core-bosons coupled to optical phonons in a lattice. At non-half-fillings, a superfluid-supersolid transition occurs at intermediate boson-phonon couplings, while at strong-couplings the system phase separates. We demonstrate explicitly that the presence of next-nearest-neighbor hopping and nearest-neighbor repulsion leads to supersolidity. Thus we present a microscopic mechanism for the homogeneous coexistence of charge-density-wave and superfluid orders.
Exploring supersolidity in naturally occurring and artificially designed systems has been and will continue to be an area of immense interest. Here, we study how superfluid and charge-density-wave (CDW) states cooperate or compete in a minimal model for hard-core-bosons (HCBs) coupled locally to optical phonons: a two-dimensional Bose-Holstein model. Our study is restricted to the parameter regimes of strong HCB-phonon coupling and non-adiabaticity. We use Quantum Monte Carlo simulation (involving stochastic-series-expansion technique) to study phase transitions and to investigate whether we have homogeneous or phase-separated coexistence. The effective Hamiltonian involves, besides a nearest-neighbor hopping and a nearest-neighbor repulsion, sizeable double-hopping terms (obtained from second-order perturbation). At densities not far from half-filling, in the parameter regime where the double-hopping terms are non-negligible (negligible) compared to the nearest-neighbor hopping, we get checkerboard-supersolidity (phase separation) with CDW being characterized by ordering wavevector Q⃗=(π,π)\vec{Q}=(π,π)Q​=(π,π).
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 study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest- and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.
We show that a nearest-neighbor singlet phase results (from an effective Hamiltonian) for the one-dimensional Hubbard-Holstein model in the regime of strong electron-electron and electron-phonon interactions and under nonadiabatic conditions ($t/{\ensuremath{\omega}}_{0}\ensuremath{\leqslant}1$). By mapping the system of nearest-neighbor singlets at a filling Np/N{N}_{p}/NNp​/N onto a hard-core-boson (HCB) ttt-VVV model at a filling ${N}_{p}/(N\ensuremath{-}{N}_{p})$, we demonstrate explicitly that superfluidity and charge density wave (CDW) occur mutually exclusively with the diagonal long range order manifesting itself only at one-third filling. Furthermore, we also show that the Bose-Einstein condensate (BEC) occupation number n0{n}_{0}n0​ for the singlet phase, similar to the n0{n}_{0}n0​ for a HCB tight binding model, scales as N\sqrt{N}N​; however, the coefficient of N\sqrt{N}N​ in the n0{n}_{0}n0​ for the interacting singlet phase is numerically demonstrated to be smaller.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.