One-dimensional Spinless Fermion Research Articles

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions

We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.

Quantum transport of strongly interacting fermions in one dimension far out of equilibrium

In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.

Accurate localization of Kosterlitz-Thouless-type quantum phase transitions for one-dimensional spinless fermions

We investigate the charge-density wave (CDW) transition for one-dimensional spinless fermions at half band-filling with nearest-neighbor electron transfer amplitude $t$ and interaction $V$. The model is equivalent to the anisotropic XXZ Heisenberg model for which the Bethe Ansatz provides an exact solution. For $V> V_{\rm c}= 2t$, the CDW order parameter and the single-particle gap are finite but exponentially small, as is characteristic for a Kosterlitz-Thouless transition. It is notoriously difficult to locate such infinite-order phase transitions in the phase diagram using approximate analytical and numerical approaches. Second-order Hartree-Fock theory is qualitatively applicable for all interaction strengths, and predicts the CDW transition to occur at $V_{\rm c,2}^{(2)}\approx 1.5t$. Second-order Hartree Fock theory is almost variational because the density of quasi-particle excitations is small. We apply the density-matrix renormalization group (DMRG) for periodic boundary conditions for system sizes up to 514 sites which permits a reliable extrapolation of all physical quantities to the thermodynamic limit, apart from the critical region. We investigate the ground-state energy, the gap, the order parameter, the momentum distribution, the quasi-particle density, and the density-density correlation function to locate $V_{\rm c}$ from the DMRG data. Tracing the breakdown of the Luttinger liquid and the peak in the quasi-particle density at the band edge permits us to reproduce $V_{\rm c}$ with an accuracy of one percent.

One-particle entanglement for one-dimensional spinless fermions after an interaction quantum quench

Particle entanglement provides information on quantum correlations in systems of indistinguishable particles. Here, we study the one particle entanglement entropy for an integrable model of spinless, interacting fermions both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time dependent density matrix renormalization group calculations, we numerically compute the one body reduced density matrix for the J-V model, as well as its post-quench dynamics. We include an analysis of the fermionic momentum distribution, showcasing its time evolution after a quantum quench. Our numerical results, extrapolated to the thermodynamic limit, can be compared with field theoretic bosonization in the Tomonaga-Luttinger liquid regime. Excellent agreement is obtained using an interaction cutoff that can be determined uniquely in the ground state.

Stability against three-body clustering in one-dimensional spinless p -wave fermions

We theoretically investigate in-medium two- and three-body correlations in one-dimensional spinless fermions with attractive two-body p-wave interaction. By investigating the variational problem of two- and three-body states above the Fermi sea, we elucidate the fate of the in-medium two- and three-body cluster states. The one-dimensional system with the strong p-wave interaction is found to be stable against the formation of three-body clusters even in the presence of the Fermi sea, in contrast to higher-dimensional systems that suffer the strong three-body loss associated with the trimer formation.

Displacement Transformations as a Tool to Study Many-Body Localization

We obtain eigenstates of interacting disorder Hamiltonians using unitary displacement transformations that rotate the state of the system. The method generates excited states if the strength of these transformations is chosen to optimize the energy, while decreasing the energy variance. We apply the method to analyse the localization properties of one-dimensional spinless fermions with short range interactions, reaching relatively large system sizes. We quantify the degree of localization through the size and disorder dependence of the inverse participation ratio.

Certified variational quantum algorithms for eigenstate preparation

Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available numerical methods, in particular those based on variational Monte Carlo simulations, become exponentially more challenging with increasing system size. Recently quantum algorithms implemented as variational models have been proposed to accelerate such simulations. The variational ansatz states are characterized by a polynomial number of parameters devised in a way to minimize the expectation value of a given Hamiltonian, which is emulated by local measurements. In this study, we develop a means to certify the termination of variational algorithms. We demonstrate our approach by applying it to three models: the transverse field Ising model, the model of one-dimensional spinless fermions with competing interactions, and the Schwinger model of quantum electrodynamics. By means of comparison, we observe that our approach shows better performance near critical points in these models. We hence take a further step to improve the applicability and to certify the results of variational quantum simulators.

Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory.

We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.

Photoinduced High-Frequency Charge Oscillations in Dimerized Systems

Photoinduced charge dynamics in dimerized systems is studied on the basis of the exact diagonalization method and the time-dependent Schr\"odinger equation for a one-dimensional spinless-fermion model at half filling and a two-dimensional model for $\kappa$-(bis[ethylenedithio]tetrathiafulvalene)$_2$X [$\kappa$-(BEDT-TTF)$_2$X] at three-quarter filling. After the application of a one-cycle pulse of a specifically polarized electric field, the charge densities at half of the sites of the system oscillate in the same phase and those at the other half oscillate in the opposite phase. For weak fields, the Fourier transform of the time profile of the charge density at any site after photoexcitation has peaks for finite-sized systems that correspond to those of the steady-state optical conductivity spectrum. For strong fields, these peaks are suppressed and a new peak appears on the high-energy side, that is, the charge densities mainly oscillate with a single frequency, although the oscillation is eventually damped. In the two-dimensional case without intersite repulsion and in the one-dimensional case, this frequency corresponds to charge-transfer processes by which all the bonds connecting the two classes of sites are exploited. Thus, this oscillation behaves as an electronic breathing mode. The relevance of the new peak to a recently found reflectivity peak in $\kappa$-(BEDT-TTF)$_2$X after photoexcitation is discussed.

Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems.The dynamical DMRG is used to compute the linear response of a finite system to an applied AC source-drain voltage, then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the DC conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in an homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.

Statistical bubble localization with random interactions

We study one-dimensional spinless fermions with random interactions, but without any on-site disorder. We find that random interactions generically stabilize a many-body localized phase, in spite of the completely extended single-particle degrees of freedom. In the large randomness limit, we construct "bubble-neck" eigenstates having a universal area-law entanglement entropy on average, with the number of volume-law states being exponentially suppressed. We argue that this statistical localization is beyond the phenomenological local-integrals-of-motion description of many-body localization. With exact diagonalization, we confirm the robustness of the many-body localized phase at finite randomness by investigating eigenstate properties such as level statistics, entanglement/participation entropies, and nonergodic quantum dynamics. At weak random interactions, the system develops a thermalization transition when the single-particle hopping becomes dominant.

Quantum phase transition and entanglement of one-dimensional spinless fermion model

Motivated by recent developments in the field of 1D topological superconductors (TSCs), we investigate the phase transition properties of p-wave superconductor with 50 sites. In this paper, we first map the p-wave fermion model into the transverse [Formula: see text] model with an incommensurate modulated transverse field. We study the phase transition from TSC phase to Anderson localization phase by using imaginary time-evolving block decimation (TEBD) algorithm. By calculating the correlation function [Formula: see text], we numerically calculate the average correlation function in different p-wave pairing amplitude [Formula: see text]. By plotting the average correlation function versus the strength of incommensurate [Formula: see text] for [Formula: see text] and [Formula: see text], we identify the phase transition from TSC phase to Anderson localization phase [X. M. Cai et al., Phys. Rev. Lett. 110, 176403 (2013)]. Last but not least, we give an average measure of the entanglement of a single site with the rest of the system and von Neumann entropy of two boundary sites for the same parameters showing that the system possesses very strong entanglement at the critical point. The finite size effect and Majorana fermions are discussed in this paper.

Half-chain entanglement entropy in the one-dimensional spinless fermion model

We calculate the half-chain entanglement entropy of the ground state in the one-dimensional spinless fermion model. Considering a tiny corner of the Hilbert space represented by matrix product states, we efficiently find the ground state by the infinite time-evolving block decimation. The Schmidt coefficients are used to determine the half-chain entanglement entropy. Using the bond dimension scaling of the half-chain entanglement entropy, we find the critical region, which is consistent with the previous results.

Number statistics for β-ensembles of random matrices: Applications to trapped fermions at zero temperature.

Let P_{β}^{(V)}(N_{I}) be the probability that a N×Nβ-ensemble of random matrices with confining potential V(x) has N_{I} eigenvalues inside an interval I=[a,b] on the real line. We introduce a general formalism, based on the Coulomb gas technique and the resolvent method, to compute analytically P_{β}^{(V)}(N_{I}) for large N. We show that this probability scales for large N as P_{β}^{(V)}(N_{I})≈exp[-βN^{2}ψ^{(V)}(N_{I}/N)], where β is the Dyson index of the ensemble. The rate function ψ^{(V)}(k_{I}), independent of β, is computed in terms of single integrals that can be easily evaluated numerically. The general formalism is then applied to the classical β-Gaussian (I=[-L,L]), β-Wishart (I=[1,L]), and β-Cauchy (I=[-L,L]) ensembles. Expanding the rate function around its minimum, we find that generically the number variance var(N_{I}) exhibits a nonmonotonic behavior as a function of the size of the interval, with a maximum that can be precisely characterized. These analytical results, corroborated by numerical simulations, provide the full counting statistics of many systems where random matrix models apply. In particular, we present results for the full counting statistics of zero-temperature one-dimensional spinless fermions in a harmonic trap.

Large deviations of the shifted index number in the Gaussian ensemble

We show that, using the Coulomb fluid approach, we are able to derive a rate function of two variables that captures: (i) the large deviations of bulk eigenvalues; (ii) the large deviations of extreme eigenvalues (both left and right large deviations); (iii) the statistics of the fraction c of eigenvalues to the left of a position x. Thus, explains the full order statistics of the eigenvalues of large random Gaussian matrices as well as the statistics of the shifted index number. All our analytical findings are thoroughly compared with Monte Carlo simulations, obtaining excellent agreement. A summary of preliminary results has already been presented in Pérez Castillo (2014 Phys. Rev. E 90 040102) in the context of one-dimensional trapped spinless fermions in a harmonic potential.

Flux quench in a system of interacting spinless fermions in one dimension

We study a quantum quench in a one-dimensional spinless fermion model (equivalent to the XXZ spin chain), where a magnetic flux is suddenly switched off. This quench is equivalent to imposing a pulse of electric field and therefore generates an initial particle current. This current is not a conserved quantity in presence of a lattice and interactions and we investigate numerically its time-evolution after the quench, using the infinite time-evolving block decimation method. For repulsive interactions or large initial flux, we find oscillations that are governed by excitations deep inside the Fermi sea. At long times we observe that the current remains non-vanishing in the gapless cases, whereas it decays to zero in the gapped cases. Although the linear response theory (valid for a weak flux) predicts the same long-time limit of the current for repulsive and attractive interactions (relation with the zero-temperature Drude weight), larger nonlinearities are observed in the case of repulsive interactions compared with that of the attractive case.

Diffusive time-evolving block decimation method for matrix product states in one-dimensional spinless fermion systems

We describe a simple method to find the ground-state energy for many-fermion systems via a diffusive time-evolving block decimation method. Matrix product states are used as candidates for an approximate ground state. We consider fermion exchange effects caused by hopping while updating the matrix product states consistently. This method is applicable to a wide class of fermion systems. We test this method in a spinless fermion system by comparing the ground-state energy in the thermodynamic limit to the exact value.

Local density of states of the one-dimensional spinless fermion model

We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbour hopping t > 0 and interaction V in its Luttinger liquid phase −2t < V ≤ 2t. The bulk density of states and the local density of states in open chains are calculated over the full band width ∼4t with an energy resolution ≤0.08t using the dynamical density-matrix renormalization group (DDMRG) method. We also perform DDMRG simulations with a resolution of 0.01t around the Fermi energy to reveal the power-law behaviour D(ϵ) ∼ |ϵ − ϵF|α predicted by the Luttinger liquid theory for bulk and boundary density of states. The exponents α are determined using a finite-size scaling analysis of DDMRG data for lattices with up to 3200 sites. The results agree with the exact exponents given by the Luttinger liquid theory combined with the Bethe Ansatz solution. The crossover from boundary to bulk density of states is analysed. We have found that boundary effects can be seen in the local density of states at all energies, even far away from the chain edges.

Luttinger liquid physics from the infinite-system density matrix renormalization group

We study one-dimensional spinless fermions at zero and finite temperature $T$ using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution $n(k)$ function at $T=0$ can be directly observed over several orders of magnitude. At finite temperature, we show that $n(k)$ obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.