Finite Temperature Charge Research Articles

Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension

For a massive scalar field with a general curvature coupling parameter, we investigate the finite temperature contributions to the Hadamard function and to the charge and current densities in the geometry of a magnetic flux carrying generalized cosmic string embedded in ($D+1$)-dimensional locally AdS spacetime with a compactified spatial dimension. For $D=4$, the geometry on the AdS boundary, in the context of the AdS/CFT duality, corresponds to a cosmic string as a linear defect, compactified along its axis. In contrast to the case of the Minkowski bulk, the upper bound on the chemical potential does not depend on the field mass and is completely determined by the length of compact dimension and by the enclosed magnetic flux. The only nonzero components correspond to the charge density, to the azimuthal current, and to the current along the compact dimension. They are periodic functions of magnetic fluxes with the period equal to the flux quantum. The charge density is an odd function and the currents are even functions of the chemical potential. At high temperatures the influence of the gravitational field and topology on the charge density is subdominant and the leading term in the corresponding expansion coincides with that for the charge density in the Minkowski spacetime. The current densities are topology-induced quantities and their behavior at high temperatures is completely different with the linear dependence on the temperature. At small temperatures and for chemical potentials smaller than the critical value, the thermal expectation values are exponentially suppressed for both massive and massless fields.

One-dimensional long-range Falikov-Kimball model: Thermal phase transition and disorder-free localization

Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

Emergent criticality and universality class of the finite-temperature charge-density-wave transition in lattice Bose gases within optical cavities

We investigate the finite temperature charge density wave (CDW) transition of lattice Bose gases within optical cavities in the deep Mott-insulator limit. We find a new critical regime emerges at a temperature around one-half of the on-site interaction energy, where the first order CDW transition at low temperatures terminates at a critical point and changes to a second order one. By directly calculating the critical exponents and constructing the effective theory in the corresponding critical regime, we find the emergent criticality belongs to the five-dimensional Ising universality class. Direct experimental observation of the emergent criticality can be readily performed by current experimental set-ups operated in the temperature regime around half the on-site interaction energy.

Finite-temperature charge dynamics and the melting of the Mott insulator

The Mott insulator is the quintessential strongly correlated electronic state. We obtain complete insight into the physics of the two-dimensional Mott insulator by extending the slave-fermion (holon-doublon) description to finite temperatures. We first benchmark its predictions against state-of-the-art quantum Monte Carlo simulations, demonstrating quantitative agreement. Qualitatively, the short-ranged spin fluctuations both induce holon-doublon bound states and renormalize the charge sector to form the Hubbard bands. The Mott gap is understood as the charge gap renormalized downwards by these spin fluctuations. As temperature increases, the Mott gap closes before the charge gap, causing a pseudogap regime to appear naturally during the melting of the Mott insulator.

Principal component analysis for fermionic critical points

We use determinant Quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero temperature antiferromagnet to singlet transition in the Periodic Anderson Model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures

We illustrate how finite-temperature charge and thermal Drude weights of one-dimensional systems can be obtained from the relaxation of initial states featuring global (left–right) gradients in the chemical potential or temperature. The approach is tested for spinless interacting fermions as well as for the Fermi-Hubbard model, and the behavior in the vicinity of special points (such as half filling or isotropic chains) is discussed. We present technical details on how to implement the calculation in practice using the density matrix renormalization group and show that the non-equilibrium dynamics is often less demanding to simulate numerically and features simpler finite-time transients than the corresponding linear response current correlators; thus, new parameter regimes can become accessible. As an application, we determine the thermal Drude weight of the Hubbard model for temperatures T which are an order of magnitude smaller than those reached in the equilibrium approach. This allows us to demonstrate that at low T and half filling, thermal transport is successively governed by spin excitations and described quantitatively by the Bethe ansatz Drude weight of the Heisenberg chain.

Finite-temperature charge transport in the one-dimensional Hubbard model

We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of $\eta \gtrsim 0.25$.

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0 transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0 1D insulator the charge stiffness D(T) vanishes for T>0 and finite values of the on-site repulsion U in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T and U>0 it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0 and vanishes for U>0 is found to result from a general transition from a conductor to an insulator or resistor occurring at U=Uc=0 for all finite temperatures T>0. (At T=0 such a transition is the quantum metal to Mott–Hubbard-insulator transition.) The interplay of the η-spin SU(2) symmetry with the hidden U(1) symmetry beyond SO(4) is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.

Nonequilibrium Green’s function approach to strongly correlated few-electron quantum dots

The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's functions theory. The ground and equilibrium state is self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for the zero and finite temperature charge carrier density, the orbital-resolved distribution functions and the self-consistent total energies and spectral functions for isotropic, two-dimensional parabolic confinement as well as for the limit of large anisotropy--quasi-one-dimensional entrapment. For the considered quantum dots with N=2, 3 and 6 electrons, the analysis comprises the crossover from Fermi gas/liquid (at large carrier density) to Wigner molecule or crystal behavior (in the low-density limit).

Finite-temperature transport in finite-size Hubbard rings in the strong-coupling limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.

Curvature of levels and charge stiffness of one-dimensional spinless fermions

Combining the Bethe Ansatz with a functional deviation expansion and using an asymptotic expansion of the Bethe Ansatz equations, we compute the curvature of levels D_n at any filling for the one-dimensional lattice spinless fermion model. We use these results to study the finite temperature charge stiffness D(T). We find that the curvature of the levels obeys, in general, the relation D_n=D_0+\delta D_n, where D_0 is the zero-temperature charge stiffness and \delta D_n arises from excitations. Away from half filling and for the low-energy (gapless) eigenstates, we find that the energy levels are, in general, flux dependent and, therefore, the system behaves as an ideal conductor, with D(T) finite. We show that if gapped excitations are included the low-energy excitations feel an effective flux \Phi^{eff} which is different from what is usually expected. At half filling, we prove, in the strong interacting limit and to order 1/V (V is the nearest-neighbor Coulomb interaction), that the energy levels are flux independent. This leads to a zero value for the curvature of levels D_n and, as consequence, to D(T)=0, proving an earlier conjecture of Zotos and Prelov\v{s}ek.

Evidence for ideal insulating or conducting state in a one-dimensional integrable system.

Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low frequency conductance indicate a fundamental difference between integrable and non-integrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The non-integrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime.

Integrability and ideal conductance at finite temperatures.

We analyze the finite temperature charge stiffness $D(T&gt;0)$, using a generalization of Kohn's method, for the problem of a particle interacting with a fermionic bath in one dimension. We present analytical evidence, using the Bethe ansatz method, that $D(T&gt;0)$ is finite in the integrable case where the mass of the particle equals the mass of the fermions and numerical evidence that it vanishes in the nonintegrable case of unequal masses. We conjecture that a finite $D(T&gt;0)$ is a generic property of integrable systems.