8/3/2019 Guido Schmid and Matthias Troyer- On the Melting of Bosonic Stripes

1/4

arXiv:cond-mat/0304657v2[cond-mat.supr-con]5May2

003

On the Melting of Bosonic Stripes

Guido Schmid(1) and Matthias Troyer(1,2)(1)Theoretische Physik, Eidgenossische Technische Hochschule Zurich, CH-8093 Zurich, Switzerland

(2) Computation Laboratory, Eidgenossische Technische Hochschule Zurich, CH-8092 Zurich, Switzerland(Dated: February 2, 2008)

We use quantum Monte Carlo simulations to determine the finite temperature phase diagram andto investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core

boson model. At half filling and low temperatures the stripes melt at a first order transition. In thedoped system, the melting transitions of the smectic phase at high temperatures and the superfluidsmectic (supersolid) phase at low temperatures are either very weakly first order, or of second orderwith no clear indications for an intermediate nematic phase.

PACS numbers: 05.30Jp, 74.25.Dw, 75.10.Jm, 61.30.Cz

Stripe phases of lattice models with broken rotationaland translational symmetry can melt in two qualitativelydifferent ways. One scenario is that both symmetries canbe restored at a single first or second order transition, andthe stripes melt directly into a normal fluid or superfluidphase. The other scenario is that first the translational

symmetry is restored when the striped solid melts intoa nematic (liquid crystal) phase with broken rotationalsymmetry. The rotational symmetry is then restored ina second melting transition of the nematic phase.

This quantum lattice problem shows similarities tothe long standing problem of the melting of a two di-mensional crystal into a continuum model, where thereis also either a first order melting or the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario oftwo Kosterlitz-Thouless transitions with an interveninghexactic phase [1]. Clear results for the classical versionof this continuum problem were obtained only recently

in a simple model of hard disks [2].Current interest in quantum mechanical stripe phasesand their melting stems from the experimental observa-tion of stripes in some high-Tc superconductors [3] andfrom the question whether and how they are related tothe occurrence of high temperature superconductivity.Numerically, stripe phases have been found to be com-petitive ground states of t-J-like models [4, 5]. Analyti-cally some theories of high temperature superconductiv-ity are closely linked to the existence of stripe and ne-matic phases [6]. While it is hard to study stripe phasesin strongly correlated fermionic models, because of thenegative sign problem of quantum Monte Carlo, we can

more accurately investigate bosonic stripes using mod-ern quantum Monte Carlo algorithms [7, 8]. Such bosonicmodels can appear as effective low energy models neglect-ing nodal quasiparticles [5, 9]. Like the cuprates, thesebosonic models show competition and in some modelscoexistence of superfluidity and charge order.

In this Letter we focus on the simplest bosonic quan-tum model exhibiting stripe order and determine its finitetemperature phase diagram. We carefully investigate itsthermal and quantum melting transitions to address the

0 0.1 0.2 0.3 0.4 0.5 0.6

t/V2

2

1

0

1

2

/V2

superfluid

smectic

empty=0

superfluid smectic

b)

a)

FIG. 1: Ground-state phase diagram of the hard-core bosonHubbard model Eq. (1) as function of t/V2 and /V2. Dueto particle-hole symmetry, the phase diagram is symmetricaround the half filling line (density = 1/2 at = 2V2) andthe lower half is shown. The thick lines 1) and 2) indicatethe cuts along which we show the finite-temperature phasediagrams in Fig. 2.

question of how stripe melting occurs in a quantum modelof bosonic stripes. The particular hard-core boson Hub-bard Hamiltonian we study on a two-dimensional squarelattice is

H= t

i,j

(ai aj + ajai) + V2

i,j

ninj

i

ni, (1)

where ai (ai) is the creation (annihilation) operator for

hard-core bosons, ni = ai ai the number operator, V2 0

the next nearest neighbor Coulomb repulsions and thechemical potential. The Hamiltonian (1) is equivalent toan anisotropic spin-1/2 model with a nearest neighbor

XY-like interaction Jxy = 2t and next nearest neighborIsing interaction Jz = V2 in a magnetic field h = 2V2.

In Fig. 1 we review the ground-state phase diagram ofthis model which was previously studied by mean-field,renormalization group and local-update quantum MonteCarlo simulations [10, 11, 12]. At half filling (density =1/2 at = 2V2) the ground state is a smectic for t/V2