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arXiv:cond-mat/9912270 · Physical Review Letters

Confinement of Slave Particles in U(1) Gauge Theories of Strongly Interacting Electrons

Chetan Nayak

Published Jul 3, 2000• 40 citations
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Abstract

We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double-occupancy constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers in a particular dual action.

DOI
10.1103/physrevlett.85.178

Related papers

Comment on “Confinement of Slave Particles in U(1) Gauge Theories of Strongly Interacting Electrons”

Masaki Oshikawa

I reexamine the Nayak's criticism [Phys. Rev. Lett. 85, 178 (2000); 86, 943 (2001).] on the U(1) gauge theory approach to the strongly correlated systems. Contrary to his conclusion, the arbitrariness of the charge assignment observed by him does not contradict the possibility of a deconfinement. Should the deconfinement occur, the deconfined slave particle carries an effective fractional charge, which is independent of the arbitrary assignment but is rather determined dynamically.

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Comment on “Confinement of Slave Particles in U(1) Gauge Theories of Strongly Interacting Electrons”

Ikuo Ichinose, Tetsuo Matsui

In a recent Letter, Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase below certain critical temperature T{CSS} that depends on hole doping. We comment on the discrepancy between the results in two papers.

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We show that slave particles are always confined in U(1) gauge theories of interacting electron systems. Consequently, the low-lying degrees of freedom are different from the slave particles. This is done by constructing a dual formulation of the slave-particle representation in which the no-double-occupancy constraint becomes linear and, hence, soluble. Spin-charge separation, if it occurs, is due to the existence of solitons with fractional quantum numbers in a particular dual action.
In a recent Letter, Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase below certain critical temperature T{CSS} that depends on hole doping. We comment on the discrepancy between the results in two papers.
We reconsider the problem of separation of spin and charge in one-dimensional quantum antiferromagnets. We show that spin and charge separation in one-dimensional strongly correlated systems cannot be described by the slave-boson or fermion representation within any perturbative treatment of the interactions between the slave holons and slave spinons. The constraint of single occupancy must be implemented exactly. As a result the slave fermions and bosons are not part of the physical spectrum. Instead, the excitations that carry the separate spin and charge quantum numbers are solitons. To prove this result, it is sufficient to study the pure spinon sector in the slave-boson representation. We start with a short-range resonating-valence-bond state spin liquid mean-field theory for the frustrated antiferromagnetic spin-1/2 chain. We derive an effective theory for the fluctuations of the Affleck-Marston and Anderson order parameters. We show how to recover the phase diagram as a function of the frustration by treating the fluctuations nonperturbatively.
Strong interactions between electrons in two dimensions can realize phases where their spins and charges separate. We capture this phenomenon within a dual formulation. Focusing on square lattices, we analyze the long-wavelength structure of vortices when the microscopic particles---electrons or spinful bosons---are near half-filling. These conditions lead to a compact gauge theory of spinons and chargons, which arise as the fundamental topological defects of the low-energy vortices. The gauge theory formulation is particularly suitable for studying numerous exotic phases and transitions. We support the general analysis by an exact implementation of the duality on a coupled-wire array. Finally, we demonstrate how the latter can be exploited to construct parent Hamiltonians for fractional phases and their transitions.
Hamiltonian simulations of lattice gauge theories promise new insights into the inner workings of QCD. The rapid development of quantum computing hardware suggests that large scale simulations may soon become feasible. However, no efficient formulation suitable for simulations near the continuum limit is currently known for the non-Abelian case, and existing candidates typically feature long range interactions in the electric part of the Hamiltonian. We prove that such non- localities are unavoidable when the gauge configuration is reparametrised while preserving both the number of degrees of freedom and the fundamental commutation relations. We then attempt to mitigate this by introducing additional gauge links alongside additional constraints. Although this approach is successful in U(1), we prove that the corresponding construction is inconsistent for non-Abelian lattice gauge theories.