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Dynamics of the doped one-dimensional t-J model from quantum Monte Carlo simulations

C. Lavalle

Published Jan 1, 2003• 0 citations
Publisher

Abstract

In this work, we present results for the dynamics of the doped one-dimensional t-J model for very large systems and in a wide parameter range. These results are obtained by quantum Monte Carlo simulation based on a newly developed algorithm, the hybrid-loop Monte Carlo. Within this algorithm the loop-algorithm is used to update the spin degrees of freedom, assuring optimal efficiency, whereas the charge degrees of freedom are evolved exactly for a given spin background in the frame of the determinantal algorithm, so that both static and dynamical observables can be measured. The study of the one-particle spectral function in the whole Luttinger-liquid regime of the phase diagram shows a splitting of the spectral weight into two branches on the inverse photoemission side, in contradiction with what is expected for an ordinary metal. This feature can be understood if we assume that the elementary excitation content of the nearest-neighbor t-J model and their dispersion is the same as the one analytically obtained at J/t=2 from a t-J model with both hopping and exchange interaction decaying as 1/r². In this case the elementary excitations are spinons with charge Q=0 and spin S=1/2, holons with charge Q=-e and spin S=0, and antiholon with charge Q=2e and spin S=0. Since the antiholon has twice the mass of the holon and charge with opposite sign, holon and antiholon are not charge conjugate but two independent elementary excitations. The agreement between the analytic results derived from our assumptions and the Monte Carlo data for a wide range of parameters and for different values of doping strongly indicate, that antiholons are generic excitations in the nearest-neighbor t-J model. Since the quantum numbers of the antiholons are the same as those of for a Cooper pair, the question arises whether these new excitations are related to superconductivity, that is indeed one of the possible phases in the one-dimensional nearest-neighbor t-J model. A further study of the system in the phase-separated region shows that the spectral function is very discontinuous in the photoemission side. This feature reminds an interference scenario generated by superposition of a continuous dispersion with a regular pattern. The nature of a phase-separated regime in a simulation with periodic boundary condition can be the origin of the regular pattern.

DOI
10.18419/opus-4695

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In this work, we present results for the dynamics of the doped one-dimensional t-J model for very large systems and in a wide parameter range. These results are obtained by quantum Monte Carlo simulation based on a newly developed algorithm, the hybrid-loop Monte Carlo. Within this algorithm the loop-algorithm is used to update the spin degrees of freedom, assuring optimal efficiency, whereas the charge degrees of freedom are evolved exactly for a given spin background in the frame of the determinantal algorithm, so that both static and dynamical observables can be measured. The study of the one-particle spectral function in the whole Luttinger-liquid regime of the phase diagram shows a splitting of the spectral weight into two branches on the inverse photoemission side, in contradiction with what is expected for an ordinary metal. This feature can be understood if we assume that the elementary excitation content of the nearest-neighbor t-J model and their dispersion is the same as the one analytically obtained at J/t=2 from a t-J model with both hopping and exchange interaction decaying as 1/r². In this case the elementary excitations are spinons with charge Q=0 and spin S=1/2, holons with charge Q=-e and spin S=0, and antiholon with charge Q=2e and spin S=0. Since the antiholon has twice the mass of the holon and charge with opposite sign, holon and antiholon are not charge conjugate but two independent elementary excitations. The agreement between the analytic results derived from our assumptions and the Monte Carlo data for a wide range of parameters and for different values of doping strongly indicate, that antiholons are generic excitations in the nearest-neighbor t-J model. Since the quantum numbers of the antiholons are the same as those of for a Cooper pair, the question arises whether these new excitations are related to superconductivity, that is indeed one of the possible phases in the one-dimensional nearest-neighbor t-J model. A further study of the system in the phase-separated region shows that the spectral function is very discontinuous in the photoemission side. This feature reminds an interference scenario generated by superposition of a continuous dispersion with a regular pattern. The nature of a phase-separated regime in a simulation with periodic boundary condition can be the origin of the regular pattern.
We present in this article results of Quantum Monte Carlo simulations for the three-band Hubbard model obtained both with the grand canonical approach as well as with the T =0 formalism. A direct comparison of Quantum Monte Carlo results with experimental values for the charge-transfer gap leads to a set of parameters for the three-band Hubbard model that consistently describes salient features of the high- T c superconductors. We find long-range antiferromagnetic order in the undoped case as well as an incommensurate structure for a doping concentration of δ≈0.20. Moreover the magnetic susceptibility as a function of doping δ is in a qualitative agreement with experiments. Concerning dynamical properties, we have evaluated the spectral density [Formula: see text]. The dispersion of the state with the lowest excitation energy is in very good agreement with experimental photoemission and inverse photoemission experiments for a doping concentration of δ=0.25. In the superconducting regime, we find that the interaction vertex for the pairing correlation function in the extended s-channel shows a maximum for δ~0.20, resembling the dependence of T c on doping. This feature is not present for other symmetries of the order parameter or in other parameter regions.
Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.
Using a newly developed hybrid Monte Carlo algorithm for the nearest-neighbor (nn) $t\mathrm{\text{\ensuremath{-}}}J$ model, we show that antiholons identified in the supersymmetric inverse squared (IS) $t\mathrm{\text{\ensuremath{-}}}J$ model are clearly visible in the electron-addition spectrum of the nn $t\mathrm{\text{\ensuremath{-}}}J$ model at J=2tJ=2tJ=2t and also for J=0.5tJ=0.5tJ=0.5t, a value of experimental relevance.
On the basis of quantum Monte Carlo results the evolution of the spectral weight $A(\mathbf{k},\ensuremath{\omega})$ of the two-dimensional Hubbard model is studied from insulating to metallic behavior. As observed in recent photoemission experiments for cuprates, the electronic excitations display essentially doping-independent features; a quasiparticlelike dispersive narrow band of width of the order of the exchange interaction JJJ and a broad valence- and conduction-band background. The continuous evolution is traced back to one and the same many-body origin: the doping-dependent antiferromagnetic spin-spin correlation.
This dissertation discussed four low-dimensional systems: Hubbard ladder and its 2D extension, anisotropic Hubbard ladder, one-dimensional two-orbital t-J model, and Kondo model. All of them are of strongly correlated. Doped cuprates, as strongly correlated systems, have attracted a lot of attention in the condensed matter physics community, not just from the purely theoretical perspective, but also due to the novel applications beyond the conventional semiconductor paradigm. They display complicated phase diagram, defying the conventional rigid band theory, shaking our common sense and driving us to wrestle with many-body physics. With the aid of advanced experimental techniques such as ARPES, its various exotic electronic structure, such as waterfalls, hole pockets, Fermi arcs and kinks have been unveiled and remain open to interpretation. To attack such complicated problems, people usually build various models to mimic the CuO2 planes, which is the common feature of various cuprate compounds and is believed to be mainly responsible for their complicated properties, especially the high temperature superconductivity. In Chapter 3, we simulated the spectral properties of the 2- leg single-band Hubbard ladder and its 2-dimensional extension at and away from half-lling using the numerical tool: the combination of Cluster Perturbation Theory (CPT) with the time-dependent density matrix renormalization group method (tDMRG) as a solver. The main features of the spectrum can be described with a mean-eld dispersion, with kinks and pseudogap traced back to scattering between spin and charge degrees of freedom. As a bonus, we nd that the spectrum of hubbard ladder involves spin-polaron, the bound state of spinon and holon. Interacting one-dimensional electron systems generically behave dierent from higher dimensional systems in the sense that its low-energy excitations are described by Luttinger liquid theory as collective bosonic modes carrying spin and charge separately, the so-called spinons and holons, rather than the coherent quasi-particles in Fermi liquid theory. This phenomenon is known as spin-charge separation, an intrinsic property of 1D system. It can be thought of as a particular case of electron fractionalization. When multiple 1D chains get coupled, how the picture changes? In Chapter 4, we study the spectral function of the anisotropic 2-leg Hubbard ladder, one of the simplest multiple-chain systems. The spectrum can be understood as the scattering resultants of spinon and holons: As the inter-chain hopping is increased, the continuum in the bonding channel moves to higher energies and spinon and holon branches merge into a single coherent quasi-particle band. Simultaneously, the spectrum undergoes a crossover from a regime with two minima at incommensurate values of kx (a Mott insulator), to one with a single minimum at kx = (a band insulator). In addition, the spectrum contains a continuum of scattering states consisting of a triplon and a polaron, accompanied by the formation of bound states with higher spin 3 2 , ferromagnetic \spin bags" in which the hole can move freely. To analyze the formation of quasi-particle, we study the time-evolution of charge and spin degrees of freedom in real space after a hole is injected, which indicates that incoherent holons and spinons can emerge into polarons, that can propagate coherently, after a characterstic time . Multiorbital systems can involve Mott and Hund physics, and are rich in various phenomena, including orbital selective Mott transitions, spin-orbital separations, and pairing density wave due to the complex interplay between spin, charge and orbital degrees of freedom. Therefore, it can capture many unique features in real strongly correlated systems, such as iron pnictides and ruthenates, and thus attract a lot of investigations. In Chapter 5, we comprehensively study a one-dimensional two-orbital model at and below quarter lling, which realizes a number of unconventional phases, by means of DMRG and some analytical calculations. In particular, we nd that the system supports an extensive density wave in which excitons quasicondense with nite center-of-mass momentum. In this phase, excitons behave as hardcore bosons without charge order. In addition, excitons can pair to form biexcitons in a state that is close to a charge density wave instability. Finally, a genuine orbital-selective paired state (metallic plus spin-gapped superconductor) can be realized when pairing dominates over the interorbital repulsion. Kondo problem, as one of the most studied and best understood correlated systems, has been studied by various techniques, but the internal structure of its ground state has two deeply con icting pictures: At strong coupling limit, the system is essentially composed of a scattering center, which is a tightly bound singlet formed by the impurity and a localized electron at r0, and the remaining conduction electrons that are decoupled to the impurity and remain almost \free". At weak enough couplings, the singlet extends to the entire volume and the impurity will couple mostly to one electron at the Fermi level. In chapter 6, we provide a coherent picture to unveil the puzzle in the context of quantum information theory by deconstructing the Kondo singlet, both in real and energy space, and measuring the spin correlations between the impurity and the invididual free electron eigenstate based on two dierent measures. As a bonus, we can identify \projected natural orbitals" that can be used as a \good" approximate wavefunctions for simulations, and a quasi-order parameter that determines the crossover from weak to strong coupling regimes and furthermore oers the means to measure the Kondo screening length K. This screening length might be used to characterize the \size" of the Kondo cloud.
Using quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at small doping. The behavior of the single-particle spectral weight A(k,ω)A({\bf k},ω)A(k,ω) as a function of hopping anisotropy t⊥/tt_\perp/tt⊥​/t at intermediate interaction strength is dominated by the transition from one-band behavior at large t⊥/tt_\perp/tt⊥​/t to two-band behavior at small t⊥/tt_\perp/tt⊥​/t, although interaction effects such as band-narrowing, a shift of spectral weight to higher energies in the unoccupied antibonding band and reflected structures due to short-range antiferromagnetic correlations are also present. A single-particle gap is resolved in the intermediate t⊥/tt_\perp/tt⊥​/t Luther-Emery phase using Density Matrix Renormalization Group calculations. The dynamical spin and charge susceptibilities show features of the expected bonding-band Luttinger liquid behavior, as well as higher-energy features due to local excitations between the chains at large t⊥/tt_\perp/tt⊥​/t, and evolve towards the behavior of two uncoupled chains as t⊥/tt_\perp/tt⊥​/t is reduced. For the one hole, large t⊥/tt_\perp/tt⊥​/t case, we make a detailed comparison between the QMC data and an approximation based on local rung states. At isotropic coupling and somewhat larger doping, we find that the dispersion of the single-particle bands is essentially unrenormalized from that of the noninteracting system, and that the spin and charge response functions have features also seen in random-phase-approximation calculations.