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Journal of Physics Conference Series

Competition between superfluid order and charge-density-wave order in SU(N) disordered attractive Fermi systems

Masaru Sakaida, Norio Kawakami

Published Mar 18, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/592/1/012104

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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 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.
Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.
Systems with competing orders are of great interest in condensed matter physics. When\ntwo phases have comparable energies, novel interplay effects such can be induced by tuning an appropriate parameter. In this thesis, we study two problems of competing orders - (i) ultracold atom gases with competing superfluidity and Charge Density Wave(CDW) orders, and (ii) low dimensional antiferromagnets with Neel order competing against various disordered ground states. \n\nIn the first part of the thesis, we study the\n attractive Hubbard model which could soon be realized in ultracold atom experiments. Close to half-filling, the superfluid ground state competes with a low-lying CDW phase. We study the collective excitations of the superfluid using the Generalized Random Phase Approximation (GRPA) and strong-coupling spin wave analysis.\n The competing CDW phase manifests as a roton-like excitation. We characterize the collective mode spectrum, setting benchmarks for experiments.\n\nWe drive competition between orders by imposing superfluid flow. Superflow leads to various instabilities: in particular, we find a dynamical instability associated with CDW order. We also find a novel dynamical incommensurate instability analogous to exciton condensation in semiconductors.\n\nIn the second part, inspired by experiments on Bi3Mn4O12(NO3)(BMNO), we first study the interlayer dimer state in spin-S bilayer antiferromagnets. At a critical bilayer coupling strength, condensation of triplet excitations leads to Neel order. In describing this transition, bond operator mean field theory suffers from systematic deviations. We bridge these deviations by taking into account corrections arising from higher spin excitations. The interlayer dimer state shows a field induced Neel transition, as seen in BMNO. Our results are relevant to the quantitative modelling of spin-S dimerized systems. \n\nWe then study the J1−J2 model on the honeycomb lattice with frustrating next-nearest neighbour exchange.\n For J2>J1/6, quantum and thermal fluctuations lead to ‘lattice nematic’\nstates. For S=1/2, this lattice nematic takes the form of a valence bond solid.\n\nWith J2<J1 /6, quantum fluctuations melt Neel order so as to give rise to a field induced Neel transition. This scenario can explain the observed properties of BMNO.\n\nWe discuss implications for the honeycomb lattice Hubbard model.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
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 spontaneously symmetry breaking states in the attractive SU(NNN) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When N>2N>2N>2, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.