Self-consistent Overhauser model for the pair distribution function of an electron gas at finite temperature

We present calculations of the spin-averaged pair distribution function g(r) in a homogeneous gas of electrons moving in dimensionality D=3 or D=2 at finite temperature. The model involves the solution of a two-electron scattering problem via an effective potential, which embodies many-body effects through a self-consistent Hartree approximation, leading to two-body wave functions to be averaged over a temperature-dependent distribution of relative momentum for electron pairs. We report illustrative numerical results for g(r) in an intermediate-coupling regime and interpret them in terms of changes of short-range order with increasing temperature.     

Topological order and conformal quantum critical points

We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2+1-dimensional Yang–Mills gauge theory with a Chern–Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.     

Variational pair theory of the attractive and extended Hubbard model ind-dimensions

We present a variational approach for treating the Hubbard Hamiltonian in one, two and three dimensions. It is based on 2M-fermion wavefunctions which are allowed to form correlated spin-singlet pairs. Expressions for the ground state energy and correlation functions are derived in terms of general pair coefficient functions. The presented approach offers a convenient starting point for improved variational treatments that allow to include different specific types of pair correlations. We present first applications to the attractive and to the extended Hubbard model using a very simple ansatz for the pair coefficient functions. The ground state energy, chemical potential, order parameter, momentum distribution as well as spin-spin and density-density correlation functions follow from a system of coupled nonlinear equations that has to be solved selfconsistently. All quantities are given for arbitrary band-filling in one, two and three dimensions. Our results are compared with those of other approximations and for the one-dimensional case with the exact results of Krivnov and Ovchinnikov.     

Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength r_s≈24 from the paramagnetic to the fully spin-polarized fluid.     

Thomas-Fermi model for quasi one-dimensional finite crystals

The model presented here applies a self-consistent method to electrons in crystals, thus enabling the calculation of the effective inner potential field. For this purpose, a Thomas-Fermi (TF) type model was developed, using a “qausi” one-dimensional finite crystal—a set of equidistant infinite thin plates representing the ionic planes, spread perpendicularly to a length axis. The model is applied to a finite crystal with no external fields. This application of a “multi-centered” TF model to an entire crystal is carried out for the first time in this work; the TF model was widely used in the past for atomic and molecular calculations, but in crystals it was limited to local use such as impurities. Poisson's (non-linear) differential equation describing the problem is solved using the highly efficient Relaxation Method. A pattern of almost periodical peaks (except near the boundaries) residing at the ionic sites is obtained for the potential, as well as for the electronic local density (indicating the electrons' tendency to pack mainly near the ions).     

From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.     

Finite temperature properties of a supersolid: a RPA approach

We study in random-phase approximation the newly discovered supersolid phase of ⁴He and present in detail its finite temperature properties. ⁴He is described within a hard-core quantum lattice gas model, with nearest and next-nearest neighbour interactions taken into account. We rigorously calculate all pair correlation functions in a cumulant decoupling scheme. Our results support the importance of the vacancies in the supersolid phase. We show that in a supersolid the net vacancy density remains constant as function of temperature, contrary to the thermal activation theory. We also analyzed in detail the thermodynamic properties of a supersolid, calculated the jump in the specific heat which compares well to the recent experiments.     

Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.     

Electron correlation in two-dimensional systems: CHNC approach to finite-temperature and spin-polarization effects

Applying the classical-map hypernetted-chain method (CHNC) developed recently by Dharma-wardana and Perrot, we have studied the temperature and spin-polarization effects on electron correlation in the uniform quantum two-dimensional gas (2DEG) over a wide range of temperature T and spin-polarization ζ. The quantum fluid at the temperature T is mapped to a classical fluid at the temperature T_cf given by T_cf²=T²+T_q², where the quantum temperature T_q is determined by comparing the calculated correlation energy to that of Monte Carlo results for the fully spin-polarized quantum system at zero temperature. By the iterative solution of the modified HNC equation and the Ornstein-Zernike equation, we have obtained the pair distribution function (PDF) and correlation energy for the two-component classical 2DEG with a classical fluid temperature T_cf. The anti-parallel bridge function B₁₂(r) appearing in the modified HNC equation is determined by using the Monte Carlo correlation energy at T=0 or STLS (Singwi-Tosi-Land-Sjölander) result at T>0 and the numerical solution to the Percus-Yevick (PY) equation for the system of hard disks. By calculating the Pauli potential, the bridge function, PDFs, structure factors and correlation energy, we have shown that in some cases, the properties of the uniform quantum 2DEG depend remarkably on the temperature and spin-polarization.     

Role of the attractive intersite interaction in the extended Hubbard model

We consider the extended Hubbard model in the atomic limit on a Bethe lattice with coordination number z. By using the equations of motion formalism, the model is exactly solved for both attractive and repulsive intersite potential V. By focusing on the case of negative V, i.e., attractive intersite interaction, we study the phase diagram at finite temperature and find, for various values of the filling and of the on-site coupling U, a phase transition towards a state with phase separation. We determine the critical temperature as a function of the relevant parameters, U/|V|, n and z and we find a reentrant behavior in the plane (U/|V|, T). Finally, several thermodynamic properties are investigated near criticality.     

Conductance of bulk samples of multiwall carbon nanotubes-metal junctions

Conductance as a function of voltage and temperature was measured in junctions made of bulk samples of multiwall carbon nanotubes and metal electrodes. A clear zero bias anomaly was observed at low temperatures. The experimental results were analyzed within existing models based on Luttinger liquid and disorder theories. We find that our results are well explained using the quasi-one-dimensional disordered model.     

Large momentum part of a strongly correlated Fermi gas

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to 1/k⁴ at large k. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the 1/k⁴ tail and various physical quantities, including the pressure at thermal equilibrium and the rate of change of energy in a dynamic sweep of the inverse scattering length.     

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

Note on the massive Rarita-Schwinger field in the AdS/CFT correspondence

We consider a massive Rarita-Schwinger field on the Anti-de Sitter space and solve the corresponding equations of motion. We show that appropriate boundary terms calculated on-shell give two-point correlation functions for spin-3/2 fields of the conformal field theory on the boundary. The relation between Rarita-Schwinger field masses and conformal dimensions of corresponding operators is established.     

Cumulant approach to dynamical correlation functions at finite temperatures

A new theoretical approach, based on the introduction of cumulants, to calculate thermodynamic averages and dynamical correlation functions at finite temperatures is developed. The method is formulated in Liouville instead of Hilbert space and can be applied to operators which do not require to satisfy fermion or boson commutation relations. The application of the partitioning and projection methods for the dynamical correlation functions is considered. The present method can be applied to weakly as well as to strongly correlated systems.     

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping δ away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/δ and 1/δ, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = π (1 − δ). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/δ, the DMRG results are consistent with a true long-range order scenario for the currents and densities.     

A symmetry principle for topological quantum order

We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The major guiding principle behind our approach is that of symmetries and entanglement. These symmetries may be actual symmetries of the Hamiltonian characterizing the system, or emergent symmetries. To this end, we introduce the concept of low-dimensional Gauge-like symmetries (GLSs), and the physical conservation laws (including topological terms, fractionalization, and the absence of quasi-particle excitations) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The physical engine for TQO are topological defects associated with the restoration of GLSs. These defects propagate freely through the system and enforce TQO. Our results are strongest for gapped systems with continuous GLSs. At zero temperature, selection rules associated with the GLSs enable us to systematically construct general states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. Indices associated with these symmetries correspond to different topological sectors. All currently known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin-exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. The symmetry based framework discussed herein allows us to go beyond standard topological field theories and systematically engineer new physical models with finite temperature TQO (both Abelian and non-Abelian). Furthermore, we analyze the insufficiency of entanglement entropy (we introduce SU(N) Klein models on small world networks to make the argument even sharper), spectral structures, maximal string correlators, and fractionalization in establishing TQO. We show that Kitaev’s Toric code model and Wen’s plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain, demonstrating that despite the spectral gap in these systems the toric operator expectation values may vanish once thermal fluctuations are present. This illustrates the fact that the quantum states themselves in a particular (operator language) representation encode TQO and that the duality mappings, being non-local in the original representation, disentangle the order. We present a general algorithm for the construction of long-range string and brane orders in general systems with entangled ground states; this algorithm relies on general ground states selection rules and becomes of the broadest applicability in gapped systems in arbitrary dimensions. We exactly recast some known non-local string correlators in terms of local correlation functions. We discuss relations to problems in graph theory.     

Temperature corrections to conformal field theory

We consider finite temperature dynamical correlation functions in the interacting delta-function Bose gas. In the low-temperature limit the asymptotic behaviour of correlation functions can be determined from conformal field theory. In the present work we determine the deviations from conformal behaviour at low temperatures. Received: 14 January 1998 / Accepted: 17 March 1998     

Exchange-correlation and layer-thickness effects in quasi-two dimensional electron liquids

We demonstrate a replacement of the non-uniform sub-band density of quasi-2D electron layers by an effective uniform-slab density. Exchange, correlation and Fermi-liquid properties are determined via a mapping of the electron liquid to a classical fluid, using the hyper-netted-chain equation inclusive of bridge corrections, (i.e. the CHNC), as a function of the density, spin-polarization, layer width and the temperature. Our parameters-free theory is in good accord with quantum simulations, with effective-mass and spin-susceptibility results for 2D layers found in GaAs/AlGaAs structures.