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Register a new userThermodynamics of spin-orbit coupled bosons in two dimensions from complex Langevin
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We investigate the thermal properties of interacting spin-orbit coupled bosons with contact interactions in two spatial dimensions. To that end, we implement the complex Langevin method, motivated by the appearance of a sign problem, on a square lattice with periodic boundary conditions. We calculate the density equation of state non-perturbatively in a range of spin-orbit couplings and chemical potentials. Our results show that mean-field solutions tend to underestimate the average density, especially for stronger values of the spin-orbit coupling. Additionally, the finite nature of the simulation volume induces the formation of pseudo-condensates. These have been observed to be destroyed by the spin-orbit interactions.
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We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two dimensional optical lattice, focusing on the spin-1 spin-orbit coupled system recently realized at the Joint Quantum Institute [Campbell et. al., arXiv:1501.05984]. We find a rich quantum phase diagram, where, in addition to the conventional phases ---superfluid and insulator--- contained in the spin-$1$ Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave-vector induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a non-zero spin-orbit strength. This state is characterized by spin density wave order, which arises from the spin-$1$ nature of the system. Interactions suppress spin density wave order, and favor a superfluid textit{only} at the Brillouin zone edge. This state has spatially oscillating mean field order parameters, but a homogeneous density. We show that the spin density wave superfluid phase survives in a two dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on $^{87}$Rb, $^7$Li, and $^{41}$K.
In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction- or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken $Z_2$ inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent $z simeq 2$, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.
We study the thermodynamics of short-range interacting, two-dimensional bosons constrained to the lowest Landau level. When the temperature is higher than other energy scales of the problem, the partition function reduces to a multidimensional complex integral that can be handled by classical Monte Carlo techniques. This approach takes the quantization of the lowest Landau level orbits fully into account. We observe that the partition function can be expressed in terms of a function of a single combination of thermodynamic variables, which allows us to derive exact thermodynamic relations. We determine the asymptotic behavior of this function and compute some thermodynamic observables numerically.
We investigate the role of a repulsive s-wave interaction in the two-body problem in the presence of spin orbit couplings, motivated by current interests in exploring exotic superfluid phases in spin-orbit coupled Fermi gases. For weak spin orbit coupling where the density of states is not significantly altered, we analytically show that the high-energy states become more important in determining the binding energy when the interaction strength decreases. Consequently, tuning the interaction gives rise to a rich ground state behavior, including a zigzag of the ground state momentum or inducing transitions among the meta-stable states. By exactly solving the two-body problem for a spin-orbit coupled Fermi mixture, we demonstrate that our analysis can also apply to the case when the density of states is significantly modified by the spin-orbit coupling. Our findings pave the way for understanding and controlling the paring of fermions in the presence of spin orbit couplings.
We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase formed by virtual hopping processes of boson pairs. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first-order to a continuous transition of the dilute bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.
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