One-dimensional Half-filled Hubbard Model Research Articles

Efficient world-line-based quantum Monte Carlo method without Hubbard–Stratonovich transformation

By precisely writing down the matrix element of the local Boltzmann operator ({mathrm{e}}^{-tau h}, where h is the Hermitian conjugate pairs of off-diagonal operators), we have proposed a new path integral formulation for quantum field theory and developed a corresponding Monte Carlo algorithm. With the current formula, the Hubbard–Stratonovich transformation is not necessary, accordingly the determinant calculation is not needed, which can improve the computational efficiency. The results show that, the simulation time has the square-law scaling with system sizes, which is comparable with the usual first-principles calculations. The current formula also improves the accuracy of the Suzuki–Trotter decomposition. As an example, we have studied the one-dimensional half-filled Hubbard model at finite temperature. The obtained results are in excellent agreement with the known solutions. The new formula and Monte Carlo algorithm could be applied to various studies in future.

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.

Strong Odd Bond - Weak Even Bond Picture in the Half-Filled One-Dimensional Hubbard Model

We study the strong odd bond - weak even bond picture by measuring the bond energy and the half-chain entanglement entropy in the one-dimensional Hubbard model. By using the infinite density matrix renormalization group with matrix product operator, we obtain the ground state of the matrix product state. As a function of the bond dimension, the bond energy and the half-chain entanglement entropy support the strong odd bond - weak even bond picture. From the expectation values of the occupation number, we numerically observe that the odd - even effect appears only for the half-filling case with a finite bond dimension. Our results confirm that the matrix product operator method is successful in exploring itinerant fermionic systems.

Ultrafast transient interference in pump-probe spectroscopy of band and Mott insulators

Ultrafast pump-probe spectroscopy with high temporal and spectral resolutions provides new insight into ultrafast nonequilibrium phenomena. We propose that transient interference between pump and probe pulses is realized in pump-probe spectroscopy of band and Mott insulators, which can be observed only after recent developments of ultrafast spectroscopic techniques. A continuum structure in the excitation spectrum of band insulators is found to act as a medium for storing the spectral information of the pump pulse, and the spectrum detected by the probe pulse is interfered with by the medium, generating the transient interference in the energy domain. We also demonstrate the transient interference in the presence of electron correlations in a one-dimensional half-filled Hubbard model. Furthermore, bosons coupled to electrons additively contribute to the interference. Our finding will provide an interpretation of probe-energy-dependent oscillations recently observed in the pump-probe spectrum for a two-dimensional Mott insulator.

Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids.

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech.2014, P10010. (doi:10.1088/1742-5468/2014/10/P10010)). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 (http://arxiv.org/abs/1611.02075)).This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Symmetries and Boundary Conditions with a Twist

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. We develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion $\Theta=\pi L/2$, where $L$ is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for $L=2$--$7$ show how the breaking of symmetry affects the convergence to the $L\to\infty$ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as $L=7$, the numerical results for twisted condition are very close to the $L\to\infty$ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.

Ground state of the one-dimensional half-filled Hubbard model

We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site, , and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U 1.1, we have the opposite situation.

Effective Hamiltonian for a half-filled asymmetric ionic Hubbard chain with alternating on-site interaction

We derive an effective spin Hamiltonian for the one-dimensional half-filled asymmetric ionic Hubbard model (IHM) with alternating on-site interaction in the limit of strong repulsion. It is shown that the effective Hamiltonian is that of a spin S = 1/2 anisotropic XXZ Heisenberg chain with alternating next-nearest-neighbor (NNN) and three-spin couplings in the presence of a uniform and a staggered magnetic field.

Criticality at the Haldane-insulator charge-density-wave quantum phase transition

Exploiting the entanglement concept within a matrix-product-state based infinite density-matrix renormalization group approach, we show that the spin-density-wave and bond-order-wave ground states of the one-dimensional half-filled extended Hubbard model give way to a symmetry-protected topological Haldane state in case an additional alternating ferromagnetic spin interaction is added. In the Haldane insulator the lowest entanglement level features a characteristic twofold degeneracy. Increasing the ratio between nearest-neighbor and local Coulomb interaction $V/U$, the enhancement of the entanglement entropy, the variation of the charge, spin and neutral gaps, and the dynamical spin/density response signal a quantum phase transition to a charge-ordered state. Below a critical point, which belongs to the universality class of the tricritical Ising model with central charge 7/10, the model is critical with $c=1/2$ along the transition line. Above this point, the transition between the Haldane insulator and charge-density-wave phases becomes first order.

Influence of spin exchange anisotropy on phase diagram of the one-dimensional t-U-V-J⊥-Jz model

In this paper, we study analytically a one-dimensional half-filled Hubbard model with nearest-neighbor Coulomb repulsion (V) and anisotropic spin exchange (J⊥ ≠ Jz) via the bosonization and renormalization-group (RG) techniques, and establish the rich phase diagrams based on the charge-spin separation hypothesis in the weak-coupling regime. The spin exchange anisotropy induces a non-critical behavior of spin correlations. The result indicates that the spin exchange anisotropy has an important impact on the topological phase diagram of the 1D extended Hubbard model.

Double-pulse deexcitations in a one-dimensional strongly correlated system

We investigate the ultrafast optical response of the one-dimensional half-filled extended Hubbard model exposed to two successive laser pulses. By using the time-dependent Lanczos method, we find that following the first pulse, the excitation and deexcitation process between the ground state and excitonic states can be precisely controlled by the relative temporal displacement of the pulses. The underlying physics can be understood in terms of a modified Rabi model. Our simulations clearly demonstrate the controllability of ultrafast transition between excited and deexcited phases in strongly correlated electron systems.

Dielectric Breakdown in Spin-Polarized Mott Insulator

Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin-polarized insulator the decay rate of the ground state into excited holon-doublon pair can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as F(th)∝Δ(3/2). Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarized system.

SPIN GAPLESS BOND-ORDERED PHASE IN THE EXTENDED HUBBARD CHAIN WITH SPIN-DEPENDENT REPULSION

Using the field theoretical bosonization and renormalization group techniques, we analytically study quantum phase diagram of a one-dimensional half-filled extended Hubbard model with on-site (U) and spin-dependent nearest-neighbor interactions (V⊥, V‖) in the weak coupling regime. In the case of easy-plane anisotropy (V⊥ > V‖) and at V‖ < U/2, the existence of bond-ordered spin-density-wave phase, corresponding to spin gapless transverse magnetization located on bonds (BSDW±) is shown.

Bond-located phases driven by exchange interaction in the one-dimensional t-U-V-J model

The one-dimensional half-filled extended Hubbard model with on-site repulsion (U) and nearest-neighbor interactions including Coulomb repulsion (V) and exchange (J) is studied in the weak-coupling regime. We present a theoretical argument for the occurrence of bond-located phases. The bond–charge–density–wave (BCDW) is realized for J>0 and bond–spin–density–wave (BSDW) occurs for J<0.

Properties of the one-dimensional Hubbard model: cellular dynamical mean-fielddescription

The one-dimensional half-filled Hubbard model is considered at zero temperature withinthe cellular dynamical mean-field theory (CDMFT). By the computation of the spectralgap and the energy density with various cluster and bath sizes we examine the accuracy ofthe CDMFT in a systematic way, which proves the accurate description of theone-dimensional systems by the CDMFT with small clusters. We also calculate the spectralweights in a full range of the momentum for various interaction strengths. The results donot only account for the spin–charge separation, but they also reproduce all the features ofthe Bethe ansatz dispersions, implying that the CDMFT provides an excellentdescription of the spectral properties of low-dimensional interacting systems.

Coupling-dependent rate of energy transfer from photoexcited Mott insulators to lattice vibrations

Photoexcited states are relaxed by transferring energy to the environments. In order to study which coupling allows fast energy transfer to lattice vibrations in correlated electron systems, we calculate the time evolutions of the kinetic energies of different types and frequencies of lattice vibrations. The one-dimensional half-filled Hubbard model is augmented with electron-lattice couplings that modulate transfer integrals, site energies, and Coulomb repulsion strengths. The time-dependent Schr\odinger equation is solved for exact many-electron wave functions, and the classical equation of motion for the lattice displacements. In order to transfer energy to classical lattice vibrations that modulate transfer integrals or site energies, the translational invariance must be broken to give optical activity to an electronic excitation with wave number $\ensuremath{\pi}$ and to these lattice vibrations. On the other hand, a certain amount of energy is always transferred to lattice vibrations that modulate Coulomb repulsion strengths, irrespective of the symmetry of the ground state, as long as the corresponding electron-lattice couplings are present. In strongly correlated electron systems, these couplings can be strong, although they are usually insignificant because their effects on the equilibrium properties can be absorbed into redefinition of Coulomb repulsion strengths. We will discuss competition or collaboration between energy-transfer pathways through different types of electron-lattice couplings.

Tuning the bond-order wave phase in the half-filled extended Hubbard model

Theoretical and computational studies of the quantum phase diagram of the one-dimensional half-filled extended Hubbard model (EHM) indicate a narrow bond-order wave (BOW) phase with finite magnetic gap E-m for on-site repulsion U < U-*, the critical point, and nearest-neighbor interaction V-c approximate to U/2 near the boundary of the charge-density wave (CDW) phase. Potentials with more extended interactions that retain the EHM symmetry are shown to have a less cooperative CDW transition with higher U-* and wider BOW phase. Density-matrix renormalization group is used to obtain E-m directly as the singlet-triplet gap, with finite E-m marking the BOW boundary V-s(U). The BOW/CDW boundary V-c(U) is obtained from exact finite-size calculations that are consistent with previous EHM determinations. The kinetic energy or bond order provides a convenient new estimate of U-* based on a metallic point at V-c(U) for U < U-*. Tuning the BOW phase of half-filled Hubbard models with different intersite potentials indicates a ground state with large charge fluctuations and magnetic frustration. The possibility of physical realizations of a BOW phase is raised for Coulomb interactions.

Photoinduced Tomonaga-Luttinger-like liquid in a Mott insulator

Photoinduced metallic states in a Mott insulator are studied for the half-filled one-dimensional Hubbard model with the time-dependent density-matrix renormalization group. An irradiation of strong ac fields is found to create, in the nonequilibrium steady state, a linear dispersion in the optical spectrum (current-current correlation) reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux--Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.

Ground-state properties of the one-dimensional extended Hubbard model at half filling

The density-matrix renormalization group (DMRG) technique is used to study the ground-state properties of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U ( V) and nearest-neighbor hopping t. We calculate the static spin structure factor to consider the spin degrees of freedom. We notice a striking difference of the static spin structure factor among the spin-density-wave, charge-density-wave (CDW), and bond-order-wave (BOW) phases. Based on the results, we identify the BOW–CDW transition at small (large) U value as continuous (of first order). We also calculate the double occupancy to consider the charge degrees of freedom. For large U, the double occupancy show a discontinuous jump at the BOW–CDW critical point and it implies first-order transition. With decreasing U, the jump becomes smaller and vanishes at the tricritical point U t ≈ 5.961 t . This value is close to our previous estimation U t = 5.89 t obtained with other quantities. Consequently, the results of static spin structure factor and double occupancy support the accuracy of our ground-state phase diagram.

Phase Diagram of the One-Dimensional Half-Filled Extended Hubbard Model

We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).