Study on the coexistence of diagonal and off-diagonal long range orders in lattice Bose systems

C. E. Campbell

Brandon P. van Zyl

Anne van Otterlo, Karl-Heinz Wagenblast

The zero temperature properties of interacting two dimensional lattice bosons are investigated. We present Monte Carlo data for soft-core bosons that demonstrate the existence of a phase in which crystalline long-range order and off-diagonal long-range order (superfluidity) coexist. We comment on the difference between hard- and soft-core bosons and compare our date to mean-field results that predict a larger coexistence region. Furthermore, we determine the critical exponents for the various phase transitions.

P. M. Lam

András Sütö

This paper is a contribution to the theory of coherent crystals. We present arguments claiming that negative minima in the Fourier transform of a soft pair interaction may give rise to the coexistence of diagonal and off-diagonal long-range order at high densities, and that this coexistence may be detectable due to a periodicity seen on the off-diagonal part of the one-body reduced density matrix, without breaking translation invariance. As an illustration, we study the ground state of a homogenous system of bosons in continuous space, from the interaction retaining only the Fourier modes $v(\k)$ belonging to a single nonzero wave number $|\k|=q$. The result is a mean-field model. We prove that for $v(\k)>0$ the ground state is asymptotically fully Bose-condensed, while for $v(\k)<0$ at densities exceeding a multiple of $\hbar^2 q^2/2m|v(\k)|$ it exhibits both Bose-Einstein condensation and diagonal long-range order, and the latter can be seen on both the one- and the two-body density matrix.

András Sütö

This paper is a contribution to the theory of coherent crystals. We present arguments claiming that negative minima in the Fourier transform of a soft pair interaction may give rise to the coexistence of diagonal and off-diagonal long-range order at high densities, and that this coexistence may be detectable due to a periodicity seen on the off-diagonal part of the one-body reduced density matrix, without breaking translation invariance. As an illustration, we study the ground state of a homogenous system of bosons in continuous space, from the interaction retaining only the Fourier modes $v(\k)$ belonging to a single nonzero wave number $|\k|=q$. The result is a mean-field model. We prove that for $v(\k)>0$ the ground state is asymptotically fully Bose-condensed, while for $v(\k)<0$ at densities exceeding a multiple of $\hbar^2 q^2/2m|v(\k)|$ it exhibits both Bose-Einstein condensation and diagonal long-range order, and the latter can be seen on both the one- and the two-body density matrix.