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arXiv:cond-mat/0309296 · Physical Review B

Lightly doped dimerized spin chain in the one-dimensional t−J−J′ model

Alexander Seidel, Patrick A. Lee

Published Mar 19, 2004• 5 citations
arXivHTMLPDF

Abstract

We study the one-dimensional $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$-model in the limit of small hole doping x and small $J/t,$ ${J}^{\ensuremath{'}}/t.$ Special emphasis is put on the regime ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,$ where a spin gap is present at small doping and the undoped spin chain is strongly dimerized. Using a perturbative approach and Luttinger liquid arguments, we demonstrate for this nonintegrable class of models that the charge degrees of freedom behave as noninteracting spinless solitons in the dilute hole limit. Our approach is also used to evaluate the energy and mass renormalization of a single hole. Interestingly, the corrections of these quantities are in powers of $\sqrt{J/t}.$ At ${J}^{\ensuremath{'}}/J=0.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.

DOI
10.1103/physrevb.69.094419

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We study the one-dimensional t\ensuremath−J\ensuremath−J\ensuremath′t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}t\ensuremath−J\ensuremath−J\ensuremath′-model in the limit of small hole doping x and small J/t,J/t,J/t, J\ensuremath′/t.{J}^{\ensuremath{'}}/t.J\ensuremath′/t. Special emphasis is put on the regime J\ensuremath′/J\ensuremath≈0.5,{J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,J\ensuremath′/J\ensuremath≈0.5, where a spin gap is present at small doping and the undoped spin chain is strongly dimerized. Using a perturbative approach and Luttinger liquid arguments, we demonstrate for this nonintegrable class of models that the charge degrees of freedom behave as noninteracting spinless solitons in the dilute hole limit. Our approach is also used to evaluate the energy and mass renormalization of a single hole. Interestingly, the corrections of these quantities are in powers of J/t.\sqrt{J/t}.J/t​. At J\ensuremath′/J=0.5{J}^{\ensuremath{'}}/J=0.5J\ensuremath′/J=0.5 we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.
Sub-dimensional magnetic polarons in the one-hole doped SU(3) ttt-JJJ model
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) ttt-JJJ model, whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects, whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N) Fermi-Hubbard models on various geometries.
Injecting a single hole into a one-dimensional Heisenberg spin chain is probably the simplest case of doping a Mott insulator. The motion of such a single hole will generally induce a many-body phase shift, which can be identified by an exact sign structure of the model known as the phase string. We show that the sign structure is nontrivial even in this simplest problem, which is responsible for the essential properties of Mott physics. We find that the characteristic momentum structure, the Luttinger liquid behavior, and the quantum phase interference of the hole under a periodic boundary condition can all be attributed to it. We use the density matrix renormalization group (DMRG) numerical simulation to make a comparative study of the t–J chain and a model in which the sign structure is switched off. We further show that the key DMRG results can be reproduced by a variational wave function with incorporating the correct sign structure. Physical implications of the sign structure for doped Mott insulators in general are also discussed.
The physics of doped Mott insulators is at the heart of strongly correlated materials and is believed to constitute an essential ingredient for high-temperature superconductivity. In systems with higher SU(N)\mathrm{SU}(N)SU(N) spin symmetries, even richer magnetic ground states appear at a filling of one particle per site compared to the case of SU(2)\mathrm{SU}(2)SU(2) spins, but their fate upon doping remains largely unexplored. Here we address this question by studying a single hole in the SU(3) $t\text{\ensuremath{-}}J$ model whose undoped ground state features long-range, diagonal spin stripes. By analyzing both ground-state and dynamical properties utilizing the density matrix renormalization group, we establish the appearence of magnetic polarons consisting of chargons and flavor defects whose dynamics is constrained to a single effective dimension along the ordered diagonal. We semi-analytically describe the system using geometric string theory, where paths of hole motion are the fundamental degrees of freedom. With recent advances in the realization and control of SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models with ultracold atoms in optical lattices, our results can directly be observed in quantum gas microscopes with single-site resolution. Our work suggests the appearance of intricate ground states at finite doping constituted by emergent, coupled Luttinger liquids along diagonals, and is a first step towards exploring a wealth of physics in doped SU(N)\mathrm{SU}(N)SU(N) Fermi-Hubbard models on various geometries.
We present a unified account for the coupled single-hole and spin dynamics in the spin-gap phase of dimerized and frustrated spin chains and two-leg spin ladders. Based on the strong dimer limit of a one-dimensional t1,2,3{t}_{1,2,3}t1,2,3​-J1,2,3{J}_{1,2,3}J1,2,3​ model a diagrammatic approach is presented that employs a mapping of the spin Hamiltonian onto a pseudofermion bond-boson model. Results for the single-hole spectrum are detailed. A finite quasiparticle weight is observed and studied for a variety of system parameters. A comparison with existing exact-diagonalization data is performed and good agreement is found.
Interacting one-dimensional electron systems are generally referred to as ``Luttinger liquids,'' after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The ``spin-incoherent Luttinger liquid'' describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground state, when a Luttinger liquid is coupled to a spin bath, which effectively introduces a ``spin temperature'' through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be written as a factorized wave function, with a spin wave function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled $t\ensuremath{-}J$ chains, but also for the $t\ensuremath{-}J$-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed ``spin incoherent.''
The interplay between spin and charge degrees of freedom arising from doping a Mott insulating quantum spin liquid (QSL) has been a topic of research for several decades. Calculating properties of these fractionalized metallic states in single-band models are generally restricted to mean-field patron descriptions and small fluctuations around these states, which are insufficient for quantitative comparison of observables to measurements performed in strongly-correlated systems. In this work, we numerically study a class of correlated electronic wavefunctions which support fractionalized spin and charge excitations and which fully take into account gauge fluctuations through the enforcement of local Hilbert space constraints. By optimizing the energy of these wavefunctions against the hole-doped Fermi Hubbard Hamiltonian, we obtain a variational ansatz for describing the low-energy physics of this model. We compare measurements of hole-induced spin-spin correlation functions to measurements taken in low temperature cold-atom simulations of the Hubbard model and find quantitative agreement between the two. In particular, we demonstrate the emergence of magnetic polaron correlations in these metallic states.