One-dimensional Extended Hubbard Model Research Articles

Unusual low-temperature behavior in the half-filled band of the one-dimensional extended Hubbard model in atomic limit.

Recently, a kind of finite-temperature pseudotransition was observed in several quasi-one-dimensional models. In this work, we consider a genuine one-dimensional extended Hubbard model in the atomic limit, influenced by an external magnetic field and with the arbitrary number of particles controlled by the chemical potential. The one-dimensional extended Hubbard model in the atomic limit was initially studied in the seventies and has been investigated over the past decades, but it still surprises us today with its fascinating properties. We rigorously analyze its low-temperature behavior using the transfer matrix technique and provide accurate numerical results. Our analysis confirms that there is an anomalous behavior in the half-filled band, specifically occurring between the alternating pair (AP) and paramagnetic (PM) phases at zero temperature. Previous investigations did not deeply identify this anomalous behavior, maybe due to the numerical simplicity of the model, but from an analytical point of view this is not so easy to manipulate algebraically because one needs to solve an algebraic cubic equation. In this study, we explore this behavior and clearly distinguish the pseudotransition, which could easily be mistaken with a real phase transition. This anomalous behavior mimics features of both first- and second-order phase transitions. However, due to its nature, we cannot expect a finite-temperature phase transition in this model.

Extracting off-diagonal order from diagonal basis measurements

Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from site-resolved measurements. Here, we show that a multiscale complexity measure can pinpoint the transition to and from the bond ordered wave phase of the one-dimensional extended Hubbard model with an off-diagonal order parameter, sandwiched between diagonal charge and spin density wave phases, using only diagonal descriptors. We study the model directly in the thermodynamic limit using the recently developed variational uniform matrix product states algorithm, and draw our samples from degenerate ground states related by global spin rotations, emulating the projective measurements that are accessible in experiments. Our results will have important implications for the study of exotic phases using optical lattice experiments. Published by the American Physical Society 2024

Spectral properties of a one-dimensional extended Hubbard model from bosonization and time-dependent variational principle: Applications to one-dimensional cuprates

Spectral properties of a one-dimensional extended Hubbard model from bosonization and time-dependent variational principle: Applications to one-dimensional cuprates

Pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling

Pump-probe spectroscopy of the one-dimensional extended Hubbard model at half filling

Waterlike density anomaly in fermions

In this work we explore the one-dimensional extended Hubbard model as a fluid system modeling liquid phases of different densities. This model naturally displays two length scales of interaction, which are connected with waterlike anomalies. We analyze the density anomaly as a function of the model parameters, namely the hopping, on-site and first neighbor interactions. We show that this anomaly is present for a wide range of model parameters and is connected to a ground-state liquid–liquid critical point.

Controlling inversion and time-reversal symmetries by subcycle pulses in the one-dimensional extended Hubbard model

Owning to their high controllability, laser pulses have contributed greatly to our understanding of strongly correlated electron systems. However, typical multicycle pulses do not control the symmetry of systems, which plays an important role in the emergence of novel quantum phases. Here, we demonstrate that subcycle pulses whose oscillation is less than one period within a pulse envelope can control inversion and time-reversal symmetries in the electronic states of the one-dimensional extended Hubbard model. Using an ultrashort subcycle pulse, one can generate a steady electric current (SEC) in a photoexcited state due to an Aharonov-Bohm flux instantaneously introduced through the phase of an electric field. Consequently, time-reversal symmetry is broken. In contrast, a broad subcycle pulse does not induce SEC but instead generates electric polarization, thus breaking inversion symmetry. Both symmetry breakings in a photoexcited state can be monitored by second-harmonic generation. These findings provide a new methodology for designing the symmetries of electronic states and open up a new field of subcycle-pulse engineering.

Time-resolved single-particle spectrum of the one-dimensional extended Hubbard model after interaction quenches

We investigate the non-equilibrium dynamics of the one-dimensional extended Hubbard model after interaction quenches. In strong-coupling regime with large on-site interaction, the ground states of this model with small and large nearest-neighbor interactions are in spin-density-wave and charge-density-wave phases, respectively. Combining twisted boundary conditions with the time-dependent Lanczos method, we obtain snapshots of the time-dependent single-particle spectrum after quenches. We find that for quench within the same phase, the single-particle spectrum becomes close to that of the quenched Hamiltonian immediately after the quench. While for quench across the critical point, the afterward evolution process depends mainly on the distribution of the initial state among the eigenstates of the quenched Hamiltonian. Our finding may serve as a way to detect the phase transition in ultracold atom systems with interactions.

Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse

The elucidation of nonequilibrium states in strongly correlated systems holds the key to emergence of novel quantum phases. The nonequilibrium-induced insulator-to-metal transition is particularly interesting since it reflects the fundamental nature of competition between itinerancy and localization of the charge degrees of freedom. We investigate pulse-excited insulator-to-metal transition of the half-filled one-dimensional extended Hubbard model. Calculating the time-dependent optical conductivity with the time-dependent density-matrix renormalization group, we find that strong mono- and half-cycle pulses inducing quantum tunneling strongly suppress spectral weights contributing to the Drude weight σD, even if we introduce a large number of carriers Δnd. This is in contrast to a metallic behavior of σD∝Δnd induced by photon absorption and chemical doping. The strong suppression of σD in quantum tunneling is a result of the emergence of the Hilbert-space fragmentation, which makes pulse-excited states glassy.Received 9 February 2022Revised 15 May 2022Accepted 18 July 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032019Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLocalizationNonequilibrium statistical mechanicsOptical conductivityPhotoinduced effectQuantum statistical mechanicsPhysical Systems1-dimensional systemsGlassy systemsMott insulatorsCondensed Matter, Materials & Applied PhysicsStatistical PhysicsQuantum Information

Excitonic effects on high-harmonic generation in Mott insulators

To study excitonic effects on high-harmonic generation (HHG) in Mott insulators, we investigate pumped nonequilibrium dynamics in the one-dimensional extended Hubbard model. By employing time-dependent calculations based on the exact diagonalization and infinite time-evolving block decimation methods, we find the strong enhancement of the HHG intensity around the exciton energy. The subcycle analysis in the sub-Mott-gap regime shows that the intensity region of the time-resolved spectrum around the exciton energy splits into two levels and oscillates following the driving electric field. This excitonic dynamics is qualitatively different from the dynamics of free doublon and holon but favorably contributes to HHG in the Mott insulator.

Superconductivity in the extended Hubbard chain with three-electron density interaction

At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.

Quantum correlations, entanglement spectrum, and coherence of the two-particle reduced density matrix in the extended Hubbard model

We study the ground state properties of the one-dimensional extended Hubbard model at half-filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of $2$ fermions and perform an analysis of its quantum correlations and coherence along the different phases of the model. Specifically, we study its (i) entanglement entropy, (ii) $\ell_1$ norm of coherence, (iii) irreducible two-body cumulant matrix and (iv) entanglement spectrum. Our results show that these different properties are complementary to each other depending on the phase of the system, exhibiting peculiar behaviors such as discontinuities, maximum or minimum values at the quantum phase transitions, thus providing a qualitative view of the phase diagram of the model. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system. Moreover, from the analysis of the dominant eigenvector in the reduced state, we can relate the SS-TS transition to the spatial separation between the fermion pairs in the two different pairing orderings. The entanglement gap is also able to highlight a transition - at a few-body level - in the groundstate wavefunction, not discussed previously in the literature. While other quantifiers are less sensitive to few-body defects in the wavefunction, the entanglement gap can work as a magnifying glass for these, capturing such small fluctuations.

Theoretical investigation of four-body interaction in the one-dimensional extended Hubbard model

In the weak-coupling regime, we analytically investigate phase diagram of a one-dimensional half-filled extended Hubbard model with nearest neighboring four-electron interaction (Q), in addition to the usual two-electron couplings (U,V>0). The additional four-electron coupling splits independent Gaussian and spin-gap transitions and also leads to the charge-gap transition. For the positive Q, the ground state exhibits three insulating phases, charge-density-wave (CDW), spin-density-wave (SDW) and bond-spin-density-wave (BSDW). For the negative Q, the phase diagram consists of five phases, which, besides the SDW and CDW phases, contain bond-charge-density-wave (BCDW), Luttinger liquid (LL) and Luther–Emery (LE) phases.

Exploring nonequilibrium phases of photo-doped Mott insulators with generalized Gibbs ensembles

Many experiments show that strong excitations of correlated quantum materials can cause non-thermal phases without equilibrium analogues. Understanding the origin and properties of these nonequilibrium states has been challenging due to the limitations of theoretical methods for nonequilibrium strongly correlated systems. In this work, we introduce a generalized Gibbs ensemble description that enables a systematic analysis of the long-time behavior of photo-doped states in Mott insulators based on equilibrium methods. We demonstrate the power of the method by mapping out the nonequilibrium phase diagram of the one-dimensional extended Hubbard model, which features η-pairing and charge density wave phases in a wide photo-doping range. We furthermore clarify that the peculiar kinematics of photo-doped carriers, and the interaction between them, play an essential role in the formation of these non-thermal phases. Our results establish a new path for the systematic analysis of nonequilibrium strongly correlated systems.

Nonequilibrium optical response of a one-dimensional Mott insulator

We define, compute and analyze the nonequilibrium differential optical conductivity of the one-dimensional extended Hubbard model at half-filling after applying a pump pulse, using the time-dependent density matrix renormalization group method. The melting of the Mott insulator is accompanied by a suppression of the local magnetic moment and ensuing photogeneration of doublon-holon pairs. The differential optical conductivity reveals $(i)$ mid-gap states related to parity-forbidden optical states, and $(ii)$ strong renormalization and hybridization of the excitonic resonance and the absorption band, yielding a Fano resonance. We offer evidence and interpret such a resonance as a signature of nonequilibrium optical excitations resembling excitonic strings, (bi)excitons, and unbound doublon-holon pairs, depending on the magnitude of the intersite Coulomb repulsion. We discuss our results in the context of pump and probe spectroscopy experiments on organic Mott insulators.

One-Dimensional Alternating Extended Hubbard Model at Quarter-Filling and Its Applications to Structural Instabilities of Organic Conductors

The one-dimensional extended Hubbard model with lattice dimerization and alternated site potentials is analyzed using the renormalization group method. The coupling of electrons to structural degrees of freedom such as the anion lattice and acoustic phonons is investigated to obtain the possible instabilities against the formation of lattice superstructures. Applications of the theory to anionic and spin-Peierls instabilities in the Fabre and Bechgaard salts series of organic conductors and ordered alloys are presented and discussed.

Characterization of photoexcited states in the half-filled one-dimensional extended Hubbard model assisted by machine learning

Photoinduced nonequilibrium states can provide new insight into dynamical properties of strongly correlated electron systems. One of the typical and extensively studied systems is the half-filled one-dimensional extended Hubbard model (1DEHM). Here, we propose that the supervised machine learning (ML) can provide useful information for characterizing photoexcited states in 1DEHM. Using entanglement spectra as a training dataset, we construct neural network. Judging from the trained network, we find that bond-spin-density wave (BSDW) order can be enhanced in photoexcited states if the frequency of a driving pulse nearly resonates with gap. We separately calculate the time evolution of local and non-local order parameters and confirm that the correlation functions of BSDW are actually enhanced by photoexcitation as predicted by ML. The successful prediction of BSDW demonstrates the advantage of ML to assist characterizing photoexcited quantum states.

Analysis of time-resolved single-particle spectrum on the one-dimensional extended Hubbard model

We investigate the short-time evolution of the half filled one-dimensional extended Hubbard model in the strong-coupling regime, driven by a transient laser pump. Combining twisted boundary conditions with the time-dependent Lanczos technique, we obtain snapshots of the single-particle spectral function with high momentum resolution. The analysis of the oscillations of the spectral function shows that its characteristic frequencies are consistent with the magnitudes of the optical gap. Furthermore, we examine the time-evolving spectral structure in the charge-density-wave phase in detail and find that one of the bands in the single-particle spectrum originates from the photoinduced bond-order background.

Nonadiabatic quantum fluctuations in the neutral ground state of tetrathiafulvalene- p -chloranil

A nonadiabatic resonating Hartree-Fock method is applied to the one-dimensional extended Hubbard model with a staggered site-diagonal potential and Su-Schrieffer-Heeger-type electron-phonon coupling to clarify the lattice and electronic structures in the charge-density-wave (CDW) ground state. It is shown that small spin-Peierls-type domains and large dimerized CDW domains appear in the main CDW state having an equidistant lattice. Interference of breathing and translational motions of these domains constitutes quantum fluctuations. The natures of different domains are analyzed by L\owdin-Feshbach partitioning method. The present results, indicating the domains in the CDW ground state as quantum fluctuations, are consistent with the experimentally observed THz electric-field-induced changes in the electronic dipole moment in the neutral phase of tetrathiafulvalene-$p$-chloranil (TTF-CA).

Photoinduced enhancement of bond order in the one-dimensional extended Hubbard model

We investigate the real-time dynamics of the half-filled one-dimensional extended Hubbard model in the strong-coupling regime, when driven by a transient laser pulse. Starting from a wide regime displaying a charge-density wave in equilibrium, a robust photoinduced in-gap state appears in the optical conductivity, depending on the parameters of the pulse. Here, by tuning its conditions, we maximize the overlap of the time-evolving wavefunction with excited states displaying the elusive bond-ordered wave of this model. Finally, we make a clear connection between the emergence of this order and the formation of the aforementioned in-gap state, suggesting the potential observation of purely electronic (i.e., not associated with a Peierls instability) bond-ordered waves in experiments involving molecular crystals.

Quantum Entanglement in Ground State of Extended Hubbard Model

Metal-insulator and CDW-SDW transitions are studied in the one-dimensional Extended Hubbard Model at half-filling by analysing the behaviour of local entanglement in fermionic systems. 1D traditional Hubbard model exhibits metal-insulator transition at critical point Uc = 0, where local entanglement reaches its maximum value. Moreover, a transition between charge- and spin-density- wave (CDW-SDW) occurs in 1D Extended Hubbard Model tUV with long-range interaction at straight line U = 2 V. The analysis of our obtained results shows that CDW-SDW transition has curious properties whose can be used in quantum information processing.