Hubbard Chain Research Articles

Bloch oscillations in a Bose–Hubbard chain with single-particle losses

We theoretically investigate Bloch oscillations in a one-dimensional Bose–Hubbard chain, with single-particle losses from the odd lattice sites described by a Lindblad equation. For a single particle the time evolution of the state is completely determined by a non-Hermitian effective Hamiltonian. We analyse the spectral properties of this Hamiltonian for an infinite lattice and link features of the spectrum to observable dynamical effects, such as frequency doubling in breathing modes. We further consider the case of many particles in the mean-field limit leading to complex nonlinear Schrödinger dynamics. Analytic expressions are derived for the generalised nonlinear stationary states and the nonlinear Bloch bands. The interplay of nonlinearity and particle losses leads to peculiar features in the nonlinear Bloch bands, such as the vanishing of solutions and the formation of additional exceptional points. The stability of the stationary states is determined via the Bogoliubov–de Gennes equation and is shown to strongly influence the mean-field dynamics. Remarkably, even far from the mean-field limit, the stability of the nonlinear Bloch bands appears to affect the quantum dynamics. This is demonstrated numerically for a two-particle system.

Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of system's physical properties. In addition, strong interactions in many-body systems strikingly affect the energy-fluctuation statistics along a non-equilibrium dynamics. By driving transient currents to oppose the precursor to metal-Mott insulator transition in a diversity of dynamical regimes, we show how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribution of finite Hubbard chains. Statistical properties of such distributions, as its skewness, that changes dramatically across the transition, can be related to irreversibility and entropy production. Even close to adiabaticity, the quasi quantum phase transition hinders equilibration, increasing the process irreversibility, and inducing strong quantum features in the quantum work distribution. In the Mott-insulating phase the work fluctuation-dissipation balance gets modified, with the irreversible entropy production dominating over work fluctuations. The effect of an interaction-driven quantum-phase-transition on thermodynamics quantities and irreversibility has to be considered in the design of protocols in small scale devices for application in quantum technology. Eventually, such many-body effects can also be employed in work extraction and refrigeration protocols at quantum scale.

Density dynamics in the mass-imbalanced Hubbard chain

We consider two mutually interacting fermionic particle species on a one-dimensional lattice and study how the mass ratio $\eta$ between the two species affects the (equilibration) dynamics of the particles. Focussing on the regime of strong interactions and high temperatures, two well-studied points of reference are given by (i) the case of equal masses ${\eta = 1}$, i.e., the standard Fermi-Hubbard chain, where initial non-equilibrium density distributions are known to decay, and (ii) the case of one particle species being infinitely heavy, ${\eta = 0}$, leading to a localization of the lighter particles in an effective disorder potential. Given these two opposing cases, the dynamics in the case of intermediate mass ratios ${0 < \eta < 1}$ is of particular interest. To this end, we study the real-time dynamics of pure states featuring a sharp initial non-equilibrium density profile. Relying on the concept of dynamical quantum typicality, the resulting non-equilibrium dynamics can be related to equilibrium correlation functions. Summarizing our main results, we observe that diffusive transport occurs for moderate values of the mass imbalance, and manifests itself in a Gaussian spreading of real-space density profiles and an exponential decay of density modes in momentum space. For stronger imbalances, we provide evidence that transport becomes anomalous on intermediate time scales and, in particular, our results are consistent with the absence of strict localization in the long-time limit for any ${\eta > 0}$. Based on our numerical analysis, we provide an estimate for the "lifetime" of the effective localization as a function of $\eta$.

Effect of mediated interactions on a Hubbard chain in mixed-dimensional fermionic cold atoms

Cold atom experiments can now realize mixtures where different components move in different spatial dimensions. We investigate a fermion mixture where one species is constrained to move along a one-dimensional lattice embedded in a two-dimensional lattice populated by another species of fermions, and where all bare interactions are contact interactions. By focusing on the one-dimensional fermions, we map this problem onto a model of fermions with non-local interactions on a chain. The effective interaction is mediated by the two-dimensional fermions and is both attractive and retarded, the form of which can be varied by changing the density of the two-dimensional fermions. By using the functional renormalization group in the weak-coupling and adiabatic limit, we show that the one-dimensional fermions can be controlled to be in various density-wave, or spin-singlet or triplet superconducting phases.

Photoinduced η -pairing at finite temperatures

We numerically prove photoinduced $\eta$-pairing in a half-filled fermionic Hubbard chain at both zero and finite temperature. The result, obtained by combining the matrix-product-state based infinite time-evolving block decimation technique and the purification method, applies to the thermodynamic limit. Exciting the Mott insulator by a laser electric field docked on via the Peierls phase, we track the time-evolution of the correlated many-body system and determine the optimal parameter set for which the nonlocal part of the $\eta$-pair correlation function becomes dominant during the laser pump at zero and low temperatures. These correlations vanish at higher temperatures and long times after pulse irradiation. In the high laser frequency strong Coulomb coupling regime we observe a remnant enhancement of the Brillouin-zone boundary pair-correlation function also at high temperatures, if the Hubbard interaction is about a multiple of the laser frequency, which can be attributed to an enhanced double occupancy in the virtual Floquet state.

Integrability of spin-[formula omitted] fermions with charge pairing and Hubbard interaction

In this paper we study the exact solution of a one-dimensional model of spin-12 electrons composed by a nearest-neighbor triplet pairing term and the on-site Hubbard interaction. We argue that this model admits a Bethe ansatz solution through a mapping to a Hubbard chain with imaginary kinetic hopping terms. The Bethe equations are similar to that found by Lieb and Wu [3] but with additional twist phases which are dependent on the ring size. We have studied the spectrum of the model with repulsive interaction by exact diagonalization and through the Bethe equations for large lattice sizes. One feature of the model is that it is possible to define the charge gap for even and odd lattice sites and both converge to the same value in the infinite size limit. We analyze the finite-size corrections to the low-lying spin excitations and argue that they are equivalent to that of the spin-12 isotropic Heisenberg model with a boundary twist depending on the lattice parity. We present the classical statistical mechanics model whose transfer matrix commutes with the model Hamiltonian. To this end we have used the construction employed by Shastry [6,7] for the Hubbard model. In our case, however, the building block is a free-fermion eight-vertex model with a particular null weight.

Entanglement and edge effects in superpositions of many-body Fock states with spatial constraints

We investigate how entangled states can be created by considering collections of point-particles arranged at different spatial configurations, i.e., Fock states with spatial constraints. This type of states can be realized in Hubbard chains of spinless hard-core bosons, at different fillings, which have gapped energy spectrum with a highly degenerate ground state. We calculate the bipartite entanglement entropy for superpositions of such Fock states and show that their entanglement can be controlled via the spatial freedom of the particles, determined by the system filling. In addition we study the effect of confinement/boundary conditions on the Fock states and show that edge modes appear at the ends of the system, when open boundary conditions are considered. Our result is an example of entangled many-body states in 1D systems of strongly interacting particles, without requiring the spin, long-range microscopic interactions or external fields. Instead, the entanglement can be tuned by the empty space in the system, which determines the spatial freedom of the interacting particles.

Many-body localization with synthetic gauge fields in disordered Hubbard chains

We analyze the localization properties of the disordered Hubbard model in the presence of a synthetic magnetic field. An analysis of level spacing ratios shows a clear transition from ergodic to many-body localized phase. The transition shifts to larger disorder strengths with increasing magnetic flux. Study of dynamics of local correlations and entanglement entropy indicates that charge excitations remain localized whereas spin degree of freedom gets delocalized in the presence of the synthetic flux. This residual ergodicity is enhanced by the presence of the magnetic field with dynamical observables suggesting incomplete localization at large disorder strengths. Furthermore, we examine the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed as opposed to the fermionic case.

{mathcal{P}}{mathcal{T}}-Symmetric Effective Model for Nonequilibrium Phase Transitions in a Dissipative Fermionic Mott Insulator Chain

Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity (boldsymbol{mathcal{P}}) and time-reversal (boldsymbol{mathcal{T}}) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the boldsymbol{mathcal{P}}boldsymbol{mathcal{T}} symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the boldsymbol{mathcal{P}}boldsymbol{mathcal{T}}-symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.

Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains.

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

Many-body localization in generalized Kondo lattice with disorder

We study the many-body localization transition in a one-dimensional generalized Kondo lattice, where a one-dimensional Hubbard chain with disordered spin-orbit coupling interacts with a fixed impurity of spin . Using exact diagonalization, we characterize the many-body localized transition with entanglement entropy and energy spectrum distribution. We find that although the subsystem of the impurity is free of disorder, it can still be localized in the spin space by the coupling with the Hubbard chain. We also investigate the out-of-time-order correlation in the many-body localized phase, and find distinctive features in comparison to either the thermal state or the Anderson localized state. Our scheme can be realized in experiments with ultracold fermions of alkaline-earth–like atoms near an orbital Feshbach resonance.

Mean-field theory for fermion pairs and the ab initio particle-vibration coupling approach

A Dyson Bethe-Salpeter equation (Dyson-BSE) for fermion pairs is presented whose kernel has a static and a one frequency dependent contribution, analogous to the self energy of the single particle Dyson equation with the (static) mean field term and the energy dependent correlation term. The static part of the Dyson-BSE is the self-consistent mean field for the vibrations. At the same time, for the correlated single particle self-energy a full particle-vibration coupling (PVC) scattering equation is established where the vibration is the same as obtained from the Dyson-BSE. Both equations, single particle Dyson equation and Dyson-BSE, are coupled through self-consistency. Numerical results for Lipkin and 1D Hubbard chain are very promising.

Time- and momentum-resolved tunneling spectroscopy of pump-driven nonthermal excitations in Mott insulators

We present a computational technique to calculate time and momentum resolved non-equilibrium spectral density of correlated systems using a tunneling approach akin scanning tunneling spectroscopy. The important difference is that our probe is extended, basically a copy of the sample, allowing one to extract the momentum information of the excitations. We illustrate the method by measuring the spectrum of a Mott-insulating extended Hubbard chain after a sudden quench with the aid of time-dependent density matrix renormalization group (tDMRG) calculations. We demonstrate that the system realizes a non-thermal state that is an admixture of spin and charge density wave states, with corresponding signatures that are recognizable as in-gap sub-bands. In particular, we identify a band of excitons and one of stable anti-bound states at high energies that gains enhanced visibility after the pump. We do not appreciate noticeable relaxation within the time-scales considered, which is attributed to the lack of decay channels due to spin-charge separation. These ideas can be readily applied to study transient dynamics and spectral signatures of correlation-driven non-equilibrium processes.

Many-body effects on the thermodynamics of closed quantum systems

Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many-body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.

Quantum magnetism of topologically-designed graphene nanoribbons

Based on the Hubbard models, quantum magnetism of topologically-designed graphene nanoribbons (GNRs) is studied using exact numerical simulations. We first study a two-band Hubbard model describing the low-energy topological bands using the density matrix renormalization group (DMRG) and determinant quantum Monte Carlo (DQMC) methods. It is found the spin correlations decay quickly with distance, and the local moment is extrapolated to zero in the presence of symmetry-breaking terms. The results show that the two-band Hubbard chain is nonmagnetic, which is in contrast to the mean-field calculation predicting a critical interaction for the magnetic transition. We then include the Hubbard interaction to the topological-designed GNRs. For large interactions, the spin correlations remain finite for all distances, and the magnetic order develops. The local moment is extrapolated to almost zero for weak interactions, and begins to increase rapidly from a critical interaction. The estimated critical value is much larger than the realistic value in graphene, and we conclude the experimentally relevant GNRs are nonmagnetic, which is consistent with the experimental results.

Suppressed energy transport in the strongly disordered Hubbard chain

We study the dynamics of the energy fluctuations in the Hubbard chain with strong potential disorder that preserves the SU(2) spin symmetry. Within the effective spin-only model that correctly captures relaxation in the situation of localized charges, we show that the decay of local energy correlations is suppressed and is at least marginally nonergodic, being qualitatively different from the subdiffusive dynamics and relaxation of local spins. The anomalous behavior can be traced back to the singular distribution of effective exchange couplings. Numerical results for the dynamical thermal conductivity within the full Hubbard model confirm that the energy (thermal) transport is closer to the charge dynamics, which appears to be also marginally localized in a wide parameter range.

Fingerprints of an orbital-selective Mott phase in the block magnetic state of BaFe2Se3 ladders

Resonant Inelastic X-Ray Scattering (RIXS) experiments on the iron-based ladder BaFe2Se3 unveiled an unexpected two-peak structure associated with local orbital (dd) excitations in a block-type antiferromagnetic phase. A mixed character between correlated band-like and localized excitations was also reported. Here, we use the density matrix renormalization group method to calculate the momentum-resolved charge- and orbital-dynamical response functions of a multi-orbital Hubbard chain. Remarkably, our results qualitatively resemble the BaFe2Se3 RIXS data, while also capturing the presence of long-range magnetic order as found in neutron scattering, only when the model is in an exotic orbital-selective Mott phase (OSMP). In the calculations, the experimentally observed zero-momentum transfer RIXS peaks correspond to excitations between itinerant and Mott insulating orbitals. We provide experimentally testable predictions for the momentum-resolved charge and orbital dynamical structures, which can provide further insight into the OSMP regime of BaFe2Se3.

Keldysh field theory of a driven dissipative Mott insulator: Nonequilibrium response and phase transitions

Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics,dynamical constraints and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady state DC transport regime and the role of dissipation in it, and electric field driven phase transitions. We develop here an effective large-N Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power-law in time, ultimately going over to an exponential decay beyond a large characteristic time that increases with N. Such a relaxation to a steady state DC response is absent in the dissipation free Hubbard chain at half filling. The steady state current at small fields is governed by large distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

We study spin transport in a Hubbard chain with strong, random, on--site potential and with spin--dependent hopping integrals, $t_{\sigma}$. For the the SU(2) symmetric case, $t_{\uparrow} =t_{\downarrow}$, such model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2) symmetry by even weak spin--asymmetry, $t_{\uparrow} \ne t_{\downarrow}$, localizes spins and restores full many-body localization. To this end we derive an effective spin model, where the spin subdiffusion is shown to be destroyed by arbitrarily weak $t_{\uparrow} \ne t_{\downarrow}$. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB2 Hubbard chains

The ground state (GS) properties of the quasi-one-dimensional AB2 Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, a functional integral representation allows us to derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and total spin per unit cell in the Lieb ferrimagnetic GS of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, including both Zeeman and orbital contributions, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.