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arXiv:1307.5726 · Physical Review A

Spin liquid phases of alkaline-earth-metal atoms at finite temperature

P. Sinkovicz, Alejandro Zamora, E. Szirmai, Maciej Lewenstein, Gergely Szirmai

Published Oct 11, 2013• 11 citations
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Abstract

We study spin liquid phases of spin-5/2 alkaline-earth-metal atoms on a honeycomb lattice at finite temperatures. Our analysis is based on a Gutzwiller projection variational approach recast to a path-integral formalism. In the framework of a saddle-point approximation we determine spin liquid phases with lowest free energy and study their temperature dependence. We identify a critical temperature, where all the spin liquid phases melt and the system goes to the paramagnetic phase. We also study the stability of the saddle-point solutions and show that a time-reversal symmetry breaking state, a so-called chiral spin liquid phase, is realized even at finite temperatures. We also determine the spin structure factor, which, in principle, is an experimentally measurable quantity and is the basic tool to map the spectrum of elementary excitations of the system.

DOI
10.1103/physreva.88.043619

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We study spin liquid phases of spin-5/2 alkaline-earth-metal atoms on a honeycomb lattice at finite temperatures. Our analysis is based on a Gutzwiller projection variational approach recast to a path-integral formalism. In the framework of a saddle-point approximation we determine spin liquid phases with lowest free energy and study their temperature dependence. We identify a critical temperature, where all the spin liquid phases melt and the system goes to the paramagnetic phase. We also study the stability of the saddle-point solutions and show that a time-reversal symmetry breaking state, a so-called chiral spin liquid phase, is realized even at finite temperatures. We also determine the spin structure factor, which, in principle, is an experimentally measurable quantity and is the basic tool to map the spectrum of elementary excitations of the system.
We propose an experimentally feasible setup with ultracold alkaline-earth-metal atoms to simulate the dynamics of U(1) lattice gauge theories in 2 +++ 1 dimensions with a Chern-Simons term. To this end we consider the ground-state properties of spin-5/2 alkaline-earth-metal fermions in a honeycomb lattice. We use the Gutzwiller projected variational approach in the strongly repulsive regime in the case of filling 1/6. The ground state of the system is a chiral spin-liquid state with $2\ensuremath{\pi}/3$ flux per plaquette, which violates time-reversal invariance. We demonstrate that due to the breaking of time-reversal symmetry the system exhibits quantum Hall effect and chiral edge states. We relate the experimentally accessible spin fluctuations to the emerging gauge-field dynamics. We discuss also properties of the lowest energy competing orders.
We theoretically investigate zero-temperature magnetic ordering of mixtures of spin-1 (alkali-metal atoms) and spin-0 (alkaline-earth-metal atoms) bosons in a three-dimensional optical lattice. With the single-mode approximation for the spin-1 bosons, we obtain an effective Bose-Hubbard model for describing the heteronuclear mixtures in optical lattices. By controlling the interspecies interactions between alkali-metal and alkaline-earth-metal atoms, we map out complete phase diagrams of the system with both positive and negative spin-dependent interactions for spin-1 atoms, based on bosonic dynamical mean-field theory. We find that the spin-1 components feature ferromagnetic and nematic insulating phases, in addition to the superfluid, depending on spin-dependent interactions. Take the spin-1 alkali-metal bosons as spin $\ensuremath{\uparrow}$, and spin-0 alkaline-earth-metal bosons as spin $\ensuremath{\downarrow}$, we observe that the system favors ferromagnetic insulator at filling n=1n=1n=1 and unorder insulator at n=2n=2n=2. Interestingly, we observe a two-step Mott-insulating-superfluid phase transition, as a result of mass imbalance between alkali-metal and alkaline-earth-metal atoms.
We explore the phase diagram of the SU(N)\mathrm{SU}(N)SU(N) Hubbard models describing fermionic alkaline-earth-metal atoms in a square optical lattice with, on average, one atom per site, using a slave rotor mean-field approach. We find that the chiral spin liquid (CSL) predicted for $N\ensuremath{\ge}5$ and large interactions passes through a fractionalized state with a spinon Fermi surface as interactions are decreased before transitioning to a weakly interacting metal. We show that by adding a uniform artificial gauge field with $2\ensuremath{\pi}/N$ flux per plaquette, the CSL becomes the ground state for all $N\ensuremath{\ge}3$ at intermediate interactions, persists to weaker interactions, and exhibits a larger spin gap. For $N\ensuremath{\ge}5$ we find the CSL is the ground state everywhere the system is a Mott insulator. The gauge field stabilization of the CSL at lower interactions, and thus at weaker lattice depths, together with the increased spin gap, can relax the temperature constraints required for its experimental realization in ultracold atom systems.
An effective model in the isolated dimer limit of the Kitaev-type model on a decorated honeycomb lattice is investigated at finite temperature. The ground state of this model is exactly shown to be a chiral spin liquid with spontaneous breaking of time reversal symmetry. We elab- orate the finite-temperature phase diagram by using the mean-field approximation and Monte Carlo simulation. We find that the phase transition between the high-temperature paramagnetic phase and the low-temperature chiral spin liquid phase is always of second order in the Monte Carlo results, although a tricritical point appears in the mean-field phase diagram. The finite-size scaling analysis of the Monte Carlo data suggests that the phase transition belongs to the two-dimensional Ising universality class.
Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.