Absence of Single-Particle Bose-Einstein Condensation at Low Densities for Bosons with Correlated Hopping

Abstract

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two dimensional model of bosons with correlated-hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated-hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed. [4]. The interplay of interaction, disorder and kinetic energy leads to the ground states that can be a superfluid, a Bose glass, a Mott insulator or a supersolid [5][6][7][8][9][10][11]. In the context of spin models too, the Schwinger boson mean-field theories provide a useful description of magnetism in the bosonic language [12][13][14][15].Over the last decade, bosons have also been used in the context of quantum magnetism to describe the magnetization process of gapped systems with a singlet ground state such as spin ladders, the triplets induced by the magnetic being treated as hard-core bosons. These bosons may condense, leading to the ordering of the transverse component of the spins, but they might as well undergo a superfluid-insulator transition, leading to magnetization plateaux [16]. For pure SU(2) interactions, and without disorder, the common belief is that the only alternative, not realized so far in quantum magnets, is a supersolid, i.e. a coexistence of these phases.In this paper, we propose that there is another possibility, namely a pairing phase without single particle Bose condensation. Our starting point is the observation that the effective bosonic model of a frustrated quantum magnet such as SrCu 2 (BO 3 ) 2 [17] contains, in addition to the usual kinetic and potential terms, a correlated-hopping term where a boson can hop only if there is another boson nearby, and that this term can be the dominant source of kinetic energy in geometries such as the orthogonal dimer model realized in SrCu 2 (BO 3 ) 2 [18,19]. While the possibility of bound state formation was already pointed out in that context, the consequences of the presence of such a term on the phase diagram at finite densities have not been worked out yet.For clarity, we concentrate in this paper on a minimal version of the model, but we have checked that the −t −t' FIG. 1: The diagonal bonds (−t′ ) denote a correlated-hopping process, and the nearest neighboring bonds denote the single particle hopping (−t).conclusions apply to the more realistic model derived for SrCu 2 (BO 3 ) 2 [20]. This model is defined on a square lattice by the Hamiltonianwhere b † r , b r are boson operators and n r = b † r b r . t and t ′ are the measures of single particle and correlated-hopping respectively. A hard core constraint that excludes multiple occupancy should in principle be included. However, we will concentrate on the low density limit, where this constraint is expected to be irrelevant. S...

Single-particle versus pair condensation of hard-core bosons with correlated hopping

“…The behavior of the largest eigenvalue λ (1) max of ρ (1) and λ (2) max of ρ (2) as function of the system size N s for constant density is decisive. For the SF phase one finds λ …”

“…In contrast, for a standard SF one has long-range two-point correlation functions and all entries of ρ (1) i,j are of the same order. For the case where all correlations are exactly the same, one can easily convince oneself that the maximum eigenvalue is of the order N s .…”

“…The behavior of ρ (2) for the different phases, we concentrate on systems with an even number of bosons at constant and low densities. Since we are limited by the size of the considered systems we use the following procedure to characterize λ (1) max and λ (2) max . We consider the maximum eigenvalues λ (1) max and λ (2) max as a function of N s and N p where we restrict N p to be even.…”

Phase Separation and Flux Quantization in the Doped Quantum Dimer Model on Square and Triangular Lattices

“…Thus, in our model, the ground-state energy has periodicity hc/2e, consistent with mobile elementary particles of charge Q = 2e in the system. Unlike what was recently found in a bosonic model with correlated hopping [16], these particles are not boson pairs: ¿From the bosonic point of view, it is the statistical flux of the dimer background that leads to the half-flux quantization. If dimers are interpreted as SU(2) electron singlets, these singlets are the physical pairs that lead to half-flux quantization.…”

Fourfold degenerate columnar-dimer ground state in square lattice antiferromagnets

“…Following Einstein's approach, we interpret the singularity in the self-consistent equations as Bose-Einstein condensation (BEC) of triplons in mode Q. This gives us a 'third' unknown in the form of triplon condensate density n c , which also resolves the problem of closure of the number of unknowns to the number of equations 44 . The physical consequence of triplon condensation, as shown later, is the emergence of non-zero local magnetic moment, giving rise to antiferromagnetic order in the system.…”