One-dimensional Fermi Research Articles

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-1/2 one-dimensional Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasi-particle transformation, by allowing for Cooper pairing to exist between all possible single-particle states, and accounts for the effects of the inhomogeneous trapping potential as well as the mean-field Hartree potential. This provides an unbiased framework to describe inhomgenous densities and pairing correlations in the FFLO state of a confined 1D gas. In a harmonic trap, numerical minimization of the HFB ground state energy yields a spatially oscillating order parameter reminiscent of the FFLO state. However, we find that this state has almost no imprint in the local fermion densities (consistent with experiments that found no evidence of the FFLO phase). In contrast, for a hard-wall geometry, we find a strong signature of the spatial oscillations of the FFLO pairing amplitude reflected in the local in situ densities. In the hard wall case, the excess spins are strongly localized near regions where there is a node in the pairing amplitude, creating an unmistakeable crystalline modulation of the density.

Distribution of entanglement Hamiltonian spectrum in free fermion models

We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the phase of the system: In the delocalized phase it is centered around very small values and in the localized phase, picks of the distribution goes to larger values. We therefore, based on the distribution of entanglement Hamiltonian eigenvalues, explain the behavior of the entanglement entropy in different phases. In addition we propose the smallest magnitude entanglement Hamiltonian eigenvalue as a characterization of phase and phase transition point (although it does not locate the phase transition point very sharply), and we verify it in the mentioned models.

Test of an Optimised Exact-Diagonalization Approach for Trapped Fermionic Mixtures

We probe the convergence of the configuration interaction (CI) approach for harmonically trapped one-dimensional Fermi–Fermi mixtures. Existing scientific papers that apply the CI approach to study such systems typically use harmonic oscillator eigenfunctions with fixed frequency parameter values as bases. We show that CI’s optimisation is the key to reducing the computational cost of the numerical study of fermionic mixtures. The effectiveness of the optimised CI approach is analysed in terms of its ability to capture the spatial fermion–fermion correlations.

Zero temperature momentum distribution of an impurity in a polaron state of one-dimensional Fermi and Tonks-Girardeau gases

We investigate the momentum distribution function of a single distinguishable impurity particle which formed a polaron state in a gas of either free fermions or Tonks-Girardeau bosons in one spatial dimension. We obtain a Fredholm determinant representation of the distribution function for the Bethe ansatz solvable model of an impurity-gas \deltaδ-function interaction potential at zero temperature, in both repulsive and attractive regimes. We deduce from this representation the fourth power decay at a large momentum, and a weakly divergent (quasi-condensate) peak at a finite momentum. We also demonstrate that the momentum distribution function in the limiting case of infinitely strong interaction can be expressed through a correlation function of the one-dimensional impenetrable anyons.

Dissipation-Induced Luttinger Liquid Correlations in a One-Dimensional Fermi Gas.

We study a one-dimensional Fermi gas in the presence of dissipative coupling to environment through the Lindblad equation. The dissipation involves energy exchange with the environment and favours the relaxation of electrons to excitations. After switching on the dissipation, the system approaches a steady state, which is described by a generalized Gibbs ensemble. The fermionic single particle density matrix resembles deceivingly to that in a hermitian interaction quench. It decays inversely with the distance for short times due to the fermionic correlations in the initial state, which changes into a noninteger power law decay for late times, representing dissipation-induced Luttinger liquid behavior. However, the crossover between the two regions occurs due to dissipation-induced damping, and is unrelated to the propagation of excitations. The velocity of information spreading is set by the dissipative coupling, and differs significantly from the original sound velocity. The thermodynamic entropy grows as -t ln t initially, and saturates to an extensive value. Our results can be tested experimentally in one-dimensional Dirac systems.

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.

Topological phases of a dimerized Fermi\u2013Hubbard model for semiconductor nano-lattices

Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s–d-hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- (α) and intermediate-temperature (α″) phases of Cd3As2, KMgBi, and rutile-structure ( beta ^{prime} -) PtO2.

Pairing patterns in one-dimensional spin-and mass-imbalanced Fermi gases

Pairing patterns in one-dimensional spin-and mass-imbalanced Fermi gases

Chiral Majorana fermion

The chiral Majorana fermion, is a massless fermionic particle being its own antiparticle, which was predicted to live in (1+1)D (i.e. one-dimensional space plus one-dimensional time) or (9+1)D. In condensed matter physics, one-dimensional (1D) chiral Majorana fermion can be viewed as the 1/2 of the chiral Dirac fermion, which could arise as the quasiparticle edge state of a two-dimensional (2D) topological state of matter. The appearance of an odd number of 1D chiral Majorana fermions on the edge implies that there exist the non-Abelian defects in the bulk. The chiral Majorana fermion edge state can be used to realize the non-Abelian quantum gate operations on electron states. Starting with the topological states in 2D, we illustrate the general and intimate relation between chiral topological superconductor and quantum anomalous Hall insulator, which leads to the theoretical prediction of the chiral Majorana fermion from the quantum anomalous Hall plateau transition in proximity to a conventional s-wave superconductor. We show that the propagation of chiral Majorana fermions leads to the same unitary transformation as that in the braiding of Majorana zero modes, and may be used for the topological quantum computation.

Thermodynamics and static response of anomalous one-dimensional fermions via a quantum Monte Carlo approach in the worldline representation

Thermodynamics and static response of anomalous one-dimensional fermions via a quantum Monte Carlo approach in the worldline representation

In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas

We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas.

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms which include local pumping and decay of particles.

Competing coherent and dissipative dynamics close to quantum criticality

We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of the system. The interplay between the critical coherent dynamics and dissipation is addressed within a dynamic finite-size scaling framework, which allows us to identify the regime where they develop a nontrivial competition. We analyze protocols that start from critical many-body ground states and put forward general dynamic scaling behaviors involving the Hamiltonian parameters and the coupling associated with the dissipation. This scaling scenario is supported by a numerical study of the dynamic behavior of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms such as local pumping, decaying, and dephasing.

Entanglement conductance as a characterization of a delocalized-localized phase transition in free fermion models

We study entanglement Hamiltonian (EH) associated with the reduced density matrix of free fermion models in delocalized-localized Anderson phase transition. We show numerically that the structure of the EH matrix differentiates the delocalized from the localizedphase. In the delocalized phase, EH becomes a long-range Hamiltonian but is short-range in the localized phase, no matter what the configuration of the system's Hamiltonian is (whether it is long or short range). With this view, we introduce the entanglement conductance (EC), which quantifies how much EH is long-range and propose it as an alternative quantity to measure entanglement in the Anderson phase transition, by which we locate the phase transition point of some one-dimensional free fermion models; and also by applying the finite size method to the EC, we find three-dimensional Anderson phase transition critical disorder strength.

Twisted and untwisted negativity spectrum of free fermions

A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

Repulsive Polarons in One-Dimensional Fermi Gases**Support by the National Natural Science Foundation of China under Grant Nos. 11374331, 11304364, and 11534014

Using the variational method, we study the properties of a spin-down impurity immersed in a one-dimensional (1D) spin-up Fermi sea. With repulsive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. We clearly calculate the binding energy, effective mass, momentum distribution, Tan contact, and pair correlation. Even in strong repulsive regimes, the results can agree with the exact Bethe Ansatz results. The repulsive polaron energy E+ is below Fermi energy EF and no negative effective masses are found in whole interaction regimes, unequal masses polarons are also calculated. We show a clear momentum distribution and calculate the Tan contact from three different aspects. Furthermore, we explore the particle-hole excitation and find that the hole terms in Fermi sea have a great influence on the polaron energy and contact in repulsive regime. These results show that the variational method can still be used effectively in 1D repulsive polaron system.

Polaronic effects in one-dimensional Fermi gas

Using the variational method and exact Bethe ansatz (BA) method, we studied the effects of an impurity immersed in a one-dimensional (1D) Fermi sea. With attractive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. For equal masses and heavy polaron systems, we calculated the binding energy, effective mass, momentum distribution and Tan contact. In the strongly attractive limit, the impurity forms a dimer with inner fermion in Fermi sea which just accords with the highly imbalanced 1D Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state in experiment. We find that the heavy impurity is dressed more deeply with Fermi sea in whole interaction regime. Furthermore, we explore the complete influence of particle-hole excitation in Fermi polaron system in 1D. We find a shocking phenomenon that the hole term in Fermi sea has a great influence on the Tan relation even in the attractive interaction regime.

Thermoelectric Power of a Luttinger Liquid

The thermoelectric power of a Luttinger liquid with a potential barrier is calculated. The long-range nature of electron–electron interaction is taken into account. It is shown that the increased interaction range changes the temperature dependence of the thermoelectric power qualitatively. At low temperatures, the Seebeck coefficient of a Luttinger liquid is considerably smaller than that of a one-dimensional Fermi gas. As the temperature increases, the thermoelectric power increases rapidly and can exceed that of a Fermi gas. The results obtained are in qualitative agreement with experimental data for quasi-one-dimensional 5-nm-thick InSb wires.

One-dimensional two-component fermions with contact even-wave repulsion and SU(2)-symmetry-breaking near-resonant odd-wave attraction

We consider a one-dimensional (1D) two-component atomic Fermi gas with contact interaction in the even-wave channel (Yang-Gaudin model) and study the effect of an SU(2) symmetry breaking near-resonant odd-wave interaction within one of the components. Starting from the microscopic Hamiltonian, we derive an effective field theory for the spin degrees of freedom using the bosonization technique. It is shown that at a critical value of the odd-wave interaction there is a first-order phase transition from a phase with zero total spin and zero magnetization to the spin-segregated phase where the magnetization locally differs from zero.