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Physical Review A

Disorder-induced charge-density-wave–superfluid transition in SU(N) Fermi systems

Masaru Sakaida, Norio Kawakami

Published Jul 31, 2014• 4 citations
Publisher

Abstract

We investigate $\mathrm{SU}(N)$ attractive Fermi systems with disorder using a Bogoliubov-de Gennes method at zero temperature with particular focus on the SU(3) case. The charge correlation function, the distribution function of the superfluid (SF) order parameter, and the free energy are calculated for a two-dimensional square lattice system at half filling. From the disorder average of these quantities, we find that disorder triggers a transition from the charge-density-wave (CDW) phase to the SF phase; disorder suppresses the CDW order, making the SF state stable. This disorder-driven phase transition is of first order and is unique for SU(3) systems; it has not been observed for the disordered SU(2) systems studied so far. We elucidate the properties of the CDW-SF transition from the disorder-averaged density of states and the distribution function of the particle density and thus obtain the ground-state phase diagram. We also address the SU(4) case and find that the CDW state is driven directly to the Anderson localized state, but the SF phase is not stabilized. We argue what will be expected for generic $N$ cases.

DOI
10.1103/physreva.90.013632

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We investigate SU(N)\mathrm{SU}(N)SU(N) attractive Fermi systems with disorder using a Bogoliubov-de Gennes method at zero temperature with particular focus on the SU(3) case. The charge correlation function, the distribution function of the superfluid (SF) order parameter, and the free energy are calculated for a two-dimensional square lattice system at half filling. From the disorder average of these quantities, we find that disorder triggers a transition from the charge-density-wave (CDW) phase to the SF phase; disorder suppresses the CDW order, making the SF state stable. This disorder-driven phase transition is of first order and is unique for SU(3) systems; it has not been observed for the disordered SU(2) systems studied so far. We elucidate the properties of the CDW-SF transition from the disorder-averaged density of states and the distribution function of the particle density and thus obtain the ground-state phase diagram. We also address the SU(4) case and find that the CDW state is driven directly to the Anderson localized state, but the SF phase is not stabilized. We argue what will be expected for generic NNN cases.
SU(N) Fermi systems with disorder are studied within the Bogoliubov-de Gennes method for the N = 3 and N = 4 cases. In our previous work[1], we focused on the properties of systems in the weakly-disordered region and found that the spatial nonuniformity caused by disorder induces the charge-density-wave(CDW)-superfluid(SF) transition. Though it was also suggested that a transition between the SF and the Anderson localized state(AL) for N = 3 and the CDW-AL transition for N = 4 would occur even in the strongly-disordered region, the nature of each phase transition was not discussed. In this paper, we present the results which were not addressed in Ref.[1] and clarify whether each of these phase transitions is of first-order or of second-order.
We study the effects of disorder on an sss-wave superfluid in the attractive Hubbard model using statistical dynamical mean-field theory, which enables us to treat both the correlation effects and the spatial nonuniformity due to disorder in the same framework. The distribution functions of the local density of states and the superfluid order parameter are obtained. From the geometrical average of these quantities, which characterizes the order parameters in disordered systems, we determine the ground-state phase diagram of the attractive Hubbard model with disorder at half-filling and zero temperature. We discuss the superfluid-localization transition and the crossover behavior within the localized phase.
We investigate the effect of white-noise disorder on the local phase stiffness and thermodynamic properties of a two-dimensional sss-wave superconductor. Starting from a local attractive model and using path-integral formalism, we derive an effective action by decoupling the superconducting order parameter into amplitude and phase components in a gauge-invariant manner. Perturbative techniques are applied to the phase fluctuation sector to derive an effective phase-only XY model for disordered superconducting systems. Solving the saddle-point Green's function using Bogoliubov-de Gennes theory, we calculate the distributions of nearest-neighbor couplings for various disorder strengths. A single-peak distribution is observed for low disorder strength, which becomes bimodal with one peak at negative couplings as the disorder strength increases. The local phase stiffness remains randomly distributed throughout the lattice and shows no correlation with pairing amplitudes. The temperature dependence of the superfluid stiffness (Js{J}_{s}Js​) is studied using Monte Carlo simulations. At strong disorder and low temperatures, Js{J}_{s}Js​ increases with increasing temperature, exhibiting anomalous behavior that may indicate the onset of a glassy transition. Additionally, calculations of the Edwards-Anderson order parameter in this disorder regime suggest the emergence of a phase-glass state at very low temperatures.
We employ the determinant quantum Monte Carlo method to study the finite-temperature properties of the half-filled attractive SU(3)\mathrm{SU}(3)SU(3) Hubbard model on a honeycomb lattice. We calculate the phase diagram in which the phase boundary separates the disordered phase and the charge density wave (CDW) phase and the transition temperature Ttr(∣U∣){T}_{\text{tr}}(|U|)Ttr​(∣U∣) varies nonmonotonically with attractive Hubbard interaction ∣U∣|U|∣U∣. As the Hubbard ∣U∣|U|∣U∣ increases at constant temperature T<max(Ttr(∣U∣))T<\text{max}({T}_{\text{tr}}(|U|))T<max(Ttr​(∣U∣)), the system first undergoes a transition from thermal Dirac semimetal phase to CDW phase, and eventually the CDW state is thermally melted at a strong Hubbard ∣U∣|U|∣U∣ where the system enters a trion liquid phase. In between the two transition points the nonmonotonic ∣U∣|U|∣U∣ dependence of CDW order strength is strikingly different from the zero-temperature monotonic behavior. In the trion CDW state where off-site trions arise from quantum fluctuations (a fermion inside an on-site trion hops to a nearest-neighbor site), the simulated triple occupancy at constant Hubbard ∣U∣|U|∣U∣ surprisingly increases with temperature, implying that the formation of off-site trions is suppressed by the thermal delocalization of on-site trions. We have also calculated the entropy-temperature relations for various attractive Hubbrad interactions, which exhibit the prominent characteristic of the Pomeranchuk effect. Our work has revealed that the formation of on-site and off-site trions has significant consequences for thermodynamic properties of SU(3) Dirac fermions.
The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with sss-wave pairing order. However, Tc{T}_{\mathrm{c}}Tc​ is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents determinant quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential Vtrap{V}_{\mathrm{trap}}Vtrap​ which makes the fermion density $\ensuremath{\rho}$ inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density $\ensuremath{\rho}(\mathbit{i})$ passes through one fermion per site. In this ring of $\ensuremath{\rho}(\mathbit{i})=1$, charge order is enhanced. A comparison is made between treating Vtrap{V}_{\mathrm{trap}}Vtrap​ within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.
Recent advances in microwave shielding have increased the stability and control of large numbers of polar molecules, allowing for the first realization of a molecular Bose-Einstein condensate. Remarkably, it was also recently realized that shielded polar molecules exhibit an SU(N) symmetry among their hyperfine states, opening the door to SU(N) systems with larger N, bosonic particle statistics, and tunable interactions-both repulsive and attractive. Motivated by these results, we have studied the SU(3) attractive Fermi-Hubbard model (FHM) on a square lattice. Using the determinant quantum Monte Carlo (DQMC) method, we explore the finite temperature phase diagram and provide evidence for three distinct regions-a three-component Fermi liquid (FL) region, a "trion" liquid (TL) region, and an ordered charge density wave (CDW) phase. The CDW phase is stable at finite temperature [in contrast to the SU(2) CDW], while the FL to TL crossover appears to point to a quantum phase transition at zero temperature. Our method extends straightforwardly to larger N and is sign problem free for even values of N. With these results, we demonstrate the potential physics enabled by using polar molecules as a quantum simulation platform for the attractive SU(N) FHM.