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Physical review. B, Condensed matter

Superconductivity of itinerant electrons coupled to spin chains

Subir Sachdev A, R. Shankar

Published Jul 1, 1988• 19 citations
Publisher

Abstract

A one-dimensional model of itinerant electrons interacting with an antiferromagnetic spin-\textonehalf{} chain is introduced and solved. The model is designed to create ferromagnetic spin polarons around each itinerant electron. The model is mapped onto a sine-Gordon Hamiltonian of three massless Bose fields. A renormalization-group analysis of the bosonic theory shows that the original model possesses quasi-long-range odd-parity superconductivity and spin-density-wave order. The relevance to high-temperature and heavy-fermion superconductors is discussed.

DOI
10.1103/physrevb.38.826

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A one-dimensional model of itinerant electrons interacting with an antiferromagnetic spin-\textonehalf{} chain is introduced and solved. The model is designed to create ferromagnetic spin polarons around each itinerant electron. The model is mapped onto a sine-Gordon Hamiltonian of three massless Bose fields. A renormalization-group analysis of the bosonic theory shows that the original model possesses quasi-long-range odd-parity superconductivity and spin-density-wave order. The relevance to high-temperature and heavy-fermion superconductors is discussed.
We consider a one-dimensional model for a ppp-wave magnet within the bosonization framework. The model consists of itinerant electrons described by an extended Hubbard model coupled to a chain of localized moments through the Kondo exchange. The classical ground state of the local-moment system captures the salient features of an odd-parity magnet. By bosonizing the coupled system, a description in terms of coupled Luttinger liquids follows, giving rise to a rich weak-coupling phase diagram. It is shown that the spin chain develops quasi long-range order consistent with the combined time-reversal and translation symmetry defining the ppp-wave magnet. We highlight the peculiar role played by this order in establishing a commensurability condition on the electronic filling under which additional interactions appear in the bosonic field theory. It is demonstrated that these interactions endow the electron spectral function with a pronounced ppp-wave character. Away from commensurate filling, these interactions are rendered irrelevant and the ensuing ppp-wave character is lost.
We construct a field-theoretic description of two coupled spin-1 Heisenberg chains, starting with the known representation of a single spin-1 chain in terms of Majorana fermions (or Ising models). After reexamining the bosonization rules for two Ising models, taking particular care of order and disorder operators, we obtain a bosonic description of the spin-1 ladder. From renormalization-group and mean-field arguments, we conclude that, for a small interchain coupling, the spin-1 ladder is approximately described by three decoupled, two-frequency sine-Gordon models. We then predict that, starting with decoupled chains, the spin gap decreases linearly with interchain coupling, in both the ferromagnetic and antiferromagnetic directions. Finally, we discuss the possibility of an incommensurate phase in the spin-1 zigzag chain.
Using the density-matrix renormalization-group method, we studied the ground state of the one-dimensional S=1S=1S=1 Bose-Hubbard model with local three-body interactions, which can be a superfluid or a Mott insulator state. We drew the phase diagram of this model for both ferromagnetic and antiferromagnetic interaction. Regardless of the sign of the spin-dependent coupling, we obtained that the Mott lobes area decreases as the spin-dependent strength increases, which means that the even-odd asymmetry of the two-body antiferromagnetic chain is absent for local three-body interactions. For antiferromagnetic coupling, we found that the density drives first-order superfluid-Mott insulator transitions for even and odd lobes. Ferromagnetic Mott insulator and superfluid states were obtained with a ferromagnetic coupling, and a tendency to a ``long-range'' order was observed.
Strongly interacting one-dimensional (1D) Bose--Fermi mixtures form a tunable XXZXXZXXZ spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions, in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.
We investigate superconductivity in a quasi-one-dimensional bipolaron system with random potentials, treating the interchain Josephson couplings in the mean-field approximation. The model is transformed into the S=(1/2 XXZ-spin chain with random fields along the z axis and the ordering field along the x axis. Using the quantum transfer-matrix method by the Suzuki-Trotter formula, we calculate the order parameter and the rigidity as functions of the temperature, the mean strength of the random fields, and the ordering field. We obtain the two-parameter scaling laws for these quantities. We also discuss these scaling relations by using the cumulant expansion in the phase Hamiltonian. This analytical method is extended to the more general models of one-dimensional interacting electrons, and the generalized susceptibilities for various long-range orderings are discussed in the light of the scaling laws.
Decades after the discovery of high-temperature superconductivity, understanding the effects of doping a Mott insulator remains a topic of great relevance, since the fundamental excitations in the normal state are not known, nor the precise origin of the pairing mechanism. In particular, the nature of the pseudogap phase at finite temperatures, above the superconducting dome, or the redistribution of spectral weight observed in experiments indicate that our knowledge is incomplete and theories may be missing some key ingredients.Due to the two-dimensionality of the problem and the limitations imposed by the Mermin-Wagner theorem, the numerical study of these questions is remarkably difficult: most treatments are either limited to small or quasi one-dimensional systems at zero temperature, or simulations may be carried out at finite temperature, completely missing the possibility for long-range order. In this dissertation, we tackle paradigmatic problems in condensed matter from a fundamentally new perspective. We numerically study interacting chains and ladders introducing RKKY-like SU(2)-symmetric long-range interactions that allow one to realize actual spontaneous symmetry breaking and true antiferromagnetic order. We shed new light on problems such as the role of magnetic order on quasi-particle formation and fractionalization, and pairing instabilities in generalized Hubbard-like models. In particular, we address questions of a very fundamental nature: (i) How do spinons evolve into magnons and what are their signatures in the excitation spectrum? (ii) how do coherent quasi-particles form in the presence of long range order? Will we still observe signatures of spin-charge separation in the spectrum? (iii) what is the interplay between long-range antiferromagnetic order and pairing? Our work offers new insight onto the role played by long-range antiferromagnetism in quasi-particle formation and pairing in the context of new toy-models that realize much of the phenomenology of their higher dimensional counterparts.--Author's abstract