Infinite On-site Repulsion Research Articles

Hilbert space fragmentation and exact scars of generalized Fredkin spin chains

In this work, based on the Fredkin spin chain, we introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction featuring a fragmented Hilbert space with coexisting quantum many-body scars. The fragmentation results from an emergent kinetic constraint resembling the conserved spin configuration in the 1D Fermi-Hubbard model in the infinite onsite repulsion limit. To demonstrate the many-body scars, we construct an exact eigenstate that is in the middle of the spectrum within each fractured sub-sector displaying either logarithmic or area-law entanglement entropy. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics by quenching different initial states that is shown through large scale matrix product state simulations. In addition, we provide a Floquet quantum circuit that displays non-ergodic dynamics as a result of sharing the same fragmentation structure and scarring as the Hamiltonian.

Effective model of one-dimensional extended Hubbard systems: Application to linear optical spectrum calculations in large systems based on many-body Wannier functions

We propose an effective model called the "charge model", for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion ($U$) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate $U$ region of $U=5-10T$, with $T$ being the nearest-neighbor electron hopping energy. These results indicate that the spin-charge separation works fairly well in this intermediate $U$ region against the usual expectation and that the charge model is an effective model that applies to actual quasi-one-dimensional materials classified as strongly correlated electron systems.

Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices

We study quantum quench dynamics in the Fermi-Hubbard model, and its $\mathrm{SU}(N)$ generalizations, in one-dimensional lattices in the limit of infinite onsite repulsion between all flavors. We consider families of initial states with generalized N\'eel order, namely, initial states in which there is a periodic $N$-spin pattern with consecutive fermions carrying distinct spin flavors. We introduce an exact approach to describe the quantum evolution of those systems, and study two unique transient phenomena that occur during expansion dynamics in finite lattices. The first one is the dynamical emergence of Gaussian one-body correlations during the melting of sharp (generalized) N\'eel domain walls. Those correlations resemble the ones in the ground state of the $\mathrm{SU}(N)$ model constrained to the same spin configurations. This is explained using an emergent eigenstate solution to the quantum dynamics. The second phenomenon is the transformation of the quasimomentum distribution of the expanding strongly interacting $\mathrm{SU}(N)$ gas into the rapidity distribution after long times. Finally, we study equilibration in $\mathrm{SU}(N)$ gasses and show that observables after equilibration are described by a generalized Gibbs ensemble. Our approach can be used to benchmark analytical and numerical calculations of dynamics of strongly correlated $\mathrm{SU}(N)$ fermions at large $U$.

Impenetrable SU(N) fermions in one-dimensional lattices

We study SU(N) fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.

Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model

Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems. This scheme allows eliminating large expansion parameters, as well as large corrections to the density matrix that generally prevent diagrammatic methods from being efficient in this regime. As an example, I compute the filling factor for the Hubbard model at infinite onsite repulsion and compare the results to controllable data obtained from Numerical Linked Cluster Expansion. I find excellent agreement between the two methods, as well as rapid convergence of the diagrammatic series. I also report results for the momentum distribution and kinetic energy of the electrons.

Phases, collective modes, and nonequilibrium dynamics of dissipative Rydberg atoms

We use a density matrix formalism to study the equilibrium phases and non-equilibrium dynamics of a system of dissipative Rydberg atoms in an optical lattice within mean-field theory. We provide equations for the fixed points of the density matrix evolution for atoms with infinite on-site repulsion and analyze these equations to obtain their Mott insulator- superfluid (MI-SF) phase boundary. A stability analysis around these fixed points provides us with the excitation spectrum of the atoms both in the MI and SF phases. We study the nature of the MI-SF critical point in the presence of finite dissipation of Rydberg excitations, discuss the fate of the superfluidity of the atoms in the presence of such dissipation in the weak-coupling limit using a coherent state representation of the density matrix, and extend our analysis to Rydberg atoms with finite on-site interaction via numerical solution of the density matrix equations. Finally, we vary the boson (atom) hopping parameter $J$ and the dissipation parameter $\Gamma$ according to a linear ramp protocol. We study the evolution of entropy of the system following such a ramp and show that the deviation of the entropy from its steady state value for the latter protocol exhibits power-law behavior as a function of the ramp time. We discuss experiments which can test our theory.

Complete spectrum of the infinite-U Hubbard ring using group theory.

We present a full analytical solution of the multiconfigurational strongly correlated mixed-valence problem corresponding to the N-Hubbard ring filled with N-1 electrons, and infinite on-site repulsion. While the eigenvalues and the eigenstates of the model are known already, analytical determination of their degeneracy is presented here for the first time. The full solution, including degeneracy count, is achieved for each spin configuration by mapping the Hubbard model into a set of Hückel-annulene problems for rings of variable size. The number and size of these effective Hückel annulenes, both crucial to obtain Hubbard states and their degeneracy, are determined by solving a well-known combinatorial enumeration problem, the necklace problem for N-1 beads and two colors, within each subgroup of the CN-1 permutation group. Symmetry-adapted solution of the necklace enumeration problem is finally achieved by means of the subduction of coset representation technique [S. Fujita, Theor. Chim. Acta 76, 247 (1989)], which provides a general and elegant strategy to solve the one-hole infinite-U Hubbard problem, including degeneracy count, for any ring size. The proposed group theoretical strategy to solve the infinite-U Hubbard problem for N-1 electrons is easily generalized to the case of arbitrary electron count L, by analyzing the permutation group CL and all its subgroups.

Energy Spectrum of the Pseudospin-Electron Model in a Dynamical Mean-Field Approach

The pseudospin-electron model in the case of infinite on-site electron repulsion is investigated. The electron energy spectrum is calculated within the framework of the dynamical mean field theory (DMFT), and the alloy analogy approximation is developed. The effect of the pseudospin-electron interaction, local asymmetry field, and tunneling-like level splitting on the existence and the number of electron subbands is investigated. The relation of the pseudospin-electron model to the problem of energy spectrum of boson-fermion mixtures in optical lattices is discussed.

Collapse of Charge Ordering Due to Disorder in Quasi One-Dimensional Electron Systems

Effects of disorder on charge ordering (CO) is investigated for one-dimensional (1D) and quasi 1D extended Hubbard model with infinite on-site repulsion at quarter filling. Only the forward scattering due to disorder is taken into account. In the 1D model, the resistivity due to Umklapp scattering that is an origin of CO is shown to be suppressed by the forward scattering. In addition, we obtain that the CO transition temperature TCO for quasi 1D model becomes smaller with increasing strength of the forward scattering.

Strongly Interacting Atom Lasers in Three-Dimensional Optical Lattices

We show that the dynamical melting of a Mott insulator in a three-dimensional lattice leads to condensation at nonzero momenta, a phenomenon that can be used to generate strongly interacting atom lasers in optical lattices. For infinite on-site repulsion, the case considered here, the momenta at which bosons condense are determined analytically and found to have a simple dependence on the hopping amplitudes. The occupation of the condensates is shown to scale linearly with the total number of atoms in the initial Mott insulator. Our results are obtained by using a Gutzwiller-type mean-field approach, gauged against exact-diagonalization solutions of small systems.

Current in Hubbard rings manipulated via magnetic flux

We study currents in a quantum ring threaded by a magnetic fluxwhich is varied in an arbitrary way from an initial constant valueϕ1 at timet1 to a final constantvalue ϕ2 at timet2. We analyze how theinduced currents for t > t2 can be controlled by the rate of flux variation . The dynamics of electrons in the ring is described using the Hubbard and the extendedHubbard models. In the Hubbard model with infinite on-site repulsion the current fort > t2 is shown to be independent of the flux variation beforet2 and is fully determined by a solution of the initial equilibrium problem and by the valueϕ2 of the flux. For intermediate values of the interaction strength the current displays regularor irregular time oscillations and the amplitude of oscillations is sensitive to the rate of theflux changing : slow changes of the flux result in small amplitudes of the current oscillations and viceversa. We demonstrate that the time dependence of the induced current bears informationon electronic correlations. Our results have important implications for not only mesoscopicrings but also the designing of quantum motors built out of ring-shaped optical lattices.

Quantum Melting of Valence-Bond Crystal Insulators and Novel Supersolid Phase at Commensurate Density

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence-Bond crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid or metallic phases under increasing hopping is investigated at T=0 K. We identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.

Cluster approach study of intersite electron correlations in pyrochlore and checkerboard lattices

To treat effects of electron correlations in geometrically frustrated pyrochlore and checkerboard lattices, an extended single-orbital Hubbard model with nearest neighbor hopping $\sim t$ and Coulomb repulsion $\sim V$ is applied. Infinite on-site repulsion, $U\to\infty$, is assumed, thus double occupancies of sites are forbidden completely in the present study. A variational Gutzwiller type approach is extended to examine correlations due to short-range $V-$interaction and a cluster approximation is developed to evaluate a variational ground state energy of the system. Obtained analytically in a special case of quarter band filling appropriate to LiV$_2$O$_4$, the resulting simple expression describes the ground state energy in the regime of intermediate and strong coupling $V$. Like in the Brinkman-Rice theory based on the standard Gutzwiller approach to the Hubbard model, the mean value of the kinetic energy is shown to be reduced strongly as the coupling $V$ approaches a critical value $V_{c}$. This finding may contribute to explaining the observed heavy fermion behavior in LiV$_2$O$_4$.

The Fröhlich-Coulomb model ofhigh-temperature superconductivity and charge segregation inthe cuprates

We introduce a generic Fröhlich-Coulomb model of the oxides,which also includes infinite on-site (Hubbard) repulsion, anddescribe a simple analytical method of solving the multi-polaronproblem in complex lattice structures. Two particular lattices,a zigzag ladder and a perovskite layer, are studied. We findthat, depending on the relative strength of the Fröhlich andCoulomb interactions, these systems are either polaronic Fermi(or Luttinger) liquids, bipolaronic superconductors, or charge-segregated insulators. In the superconducting phase the carriersare superlight mobile bipolarons. The model describes keyfeatures of the cuprates such as their Tc-values, the isotopeeffects, the normal-state diamagnetism, the pseudogap, and spectralfunctions measured in tunnelling and photoemission. We arguethat a low Fermi energy and strong coupling of carriers withhigh-frequency phonons is the cause of high criticaltemperatures in novel superconductors.

Excitons in the strong coupling limit of the one-dimensional extended Hubbard model

Excitons in the strong coupling limit of the half-filled one-dimensional extended Hubbard model with $1/r$ interactions are studied. Unlike the situation for nearest neighbor interactions, where there is at most only one (doubly degenerate) bound state, a $1/r$ interaction results in an infinite number of doubly degenerate bound states. In the continuum limit the exciton states are one-dimensional hydrogenlike states, with binding energies $\ensuremath{\sim}{1/n}^{2}.$ The particle--hole separation grows rapidly with n as ${n}^{2}.$ The binding energies are reduced on a discrete lattice. However, for conjugated systems of interest, the discrete correction to the continuum limit are small. When the infinite onsite repulsion limit is relaxed the degenerate states split, forming a doublet of even and odd parity states.

Magnetic impurity effects in metallic carbon nanotubes: local non-Fermi liquid theory

Magnetic impurity effects on metallic carbon nanotubesare studied theoretically. The resolvent method for themultichannel Kondo effect is applied to the band structureof the k · p perturbation Hamiltonian in the limit of infinite onsite repulsion at the impurity site. We discuss the local non-Fermi liquid behaviour at temperatures below the Kondo temperature TK. The density of statesof localized electrons has a singularity at about |ω|1/2,which gives rise to a pseudogap at the Kondo resonanceat low temperatures. The temperature dependence of the electronic resistivity is predicted to be T 1/2, and theimaginary part of the dynamical susceptibilities is dependent on |ω|1/2. Possible experimental observations are discussed.

Bose-Einstein condensation in an exactly solvable model of strongly interacting bosons

An exact algebraic solution is presented for the spectrum of the Bose-Hubbard model for pure systems in the limit of infinite-range hopping and infinite on-site repulsion. This strongly interacting boson system is shown to exhibit Bose-Einstein condensation into the lowest unperturbed single-particle state, with a transition temperature which, for any density of bosons, is always lower than that in the absence of interactions.

Spectrum of elementary and collective excitations in the dimerizedS=1/2Heisenberg chain with frustration

We have studied the low-energy excitation spectrum of a dimerized and frustrated antiferromagnetic Heisenberg chain. We use an analytic approach, based on a description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Additional singlet $(S=0)$ and triplet $(S=1)$ modes are found as two-particle bound states of the elementary triplets. We have also calculated the contributions of the elementary and collective excitations into the spin structure factor. Our results are in excellent agreement with exact diagonalizations and dimer series expansions data as long as the dimerization parameter \ensuremath{\delta} is not too small $(\ensuremath{\delta}>0.1),$ i.e., while the elementary triplets can be treated as localized objects.

Novel approach to description of spin liquid phases in low-dimensional quantum antiferromagnets

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the S=1 elementary excitations are described as dilute Bose gas with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg antiferromagnet. Our analytic results for the triplet gap, the excitation spectrum and the location of the quantum critical point are in excellent agreement with numerical calculations. We also discuss singlet and triplet bound states of the elementary triplets. It has been demonstrated that the existence of such bound states is an intrinsic property of the dimerized spin liquid.

Spin-wave Gap Critical Index for the Quantum Two-layer Heisenberg Antiferromagnet at T = 0

The two-layer Heisenberg antiferromagnet exhibits a zero temperature quantum phase transition from a disordered dimer phase to a collinear Neel phase, with long range order in the ground state. The spin-wave gap vanishes as Δ ∝ (J ⊥ – J ⊥ c) ν approaching the transition point. To account for strong correlations, the S = 1 elementary excitations triplets are described as a dilute Bose gas with infinite on-site repulsion. We apply the Brueckner diagram approach which gives the critical index ν ≈ 0 . 5. We demonstrate also that the linearised in density Brueckner equations give the mean field result ν = 1. Finally, an expansion of the Brueckner equations in powers of the density, combined with the scaling hypothesis, gives ν ≈ 0 . 67. This value agrees reasonably with that of the nonlinear O(3) σ model. Our approach demonstrates that for other quantum spin models the critical index can be different from that in the nonlinear σ model. We discuss the conditions for this to occur.