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arXiv:cond-mat/0206560 · Physical Review Letters

Topological Gauge Structure and Phase Diagram for Weakly Doped Antiferromagnets

Su-Peng Kou, Zheng-Yu Weng

Published Apr 17, 2003• 29 citations
arXivHTMLPDF

Abstract

We show that a topological gauge structure in an effective description of the t-J model gives rise to a global phase diagram of antiferromagnetic and superconducting phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration x(c) approximately equal to 0.043. The complex experimental phase diagram at low doping is well described within such a framework.

DOI
10.1103/physrevlett.90.157003

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We show that a topological gauge structure in an effective description of the t-J model gives rise to a global phase diagram of antiferromagnetic and superconducting phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration x(c) approximately equal to 0.043. The complex experimental phase diagram at low doping is well described within such a framework.
In the t-J model, the electron fractionalization is dictated by the phase string effect. We find that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice versa in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.
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A slave-fermion gauge-theory approach of the t-J model: Doping-induced complex magnetic structure and Z2_{2}2​ spin-gapped anomalous metal in an antiferromagnetic doped Mott insulator
We reinvestigate a doped antiferromagnetic Mott insulator based on the slave-fermion approach of the t-J model, where antiferromagnetic spin fluctuations and doped holes are described by bosonic spinons and fermionic holons, respectively. Earlier studies have shown that an effective field theory for the doped antiferromagnetic Mott insulator is given by a non-relativistic fermion (holon) U(1) gauge theory for charge dynamics and a relativistic boson (spinon) U(1) gauge theory for spin dynamics, thus allowing an anomalous metallic phase where bosonic spinons are gapped away from an antiferromagnetic state, analogous to the U(1) spin liquid phase in the slave-boson approach of the t-J model. We argue that the emergent U(1) gauge structure in this approach is based on a simplified picture for antiferromagnetic correlations. Considering that dynamics of doped holes frustrates a collinear antiferromagnetic spin configuration, we show that doped holes enhance ferromagnetic spin correlations and result in a complex magnetic structure. The presence of such a complex spin texture reduces the U(1) gauge structure down to Z2_{2}2​, thus a different effective field theory results for the spin-gapped non-Fermi liquid metal at low temperatures because there are no gapless U(1) gauge fluctuations.
A mutual Chern-Simons Lagrangian is derived as a minimal field theory description of the phase-string model for doped antiferromagnets. Such an effective Lagrangian is shown to retain the full symmetries of parity, time reversal, and global SU(2) spin rotation, in contrast to conventional Chern-Simons theories where first two symmetries are usually broken. Two ordered phases---i.e., antiferromagnetic and superconducting states---are found at low temperatures as characterized by ``dual'' Meissner effects and dual-flux-quantization conditions due to the mutual Chern-Simons gauge structure. A ``dual'' confinement in charge and spin degrees of freedom occurs such that no true spin-charge separation is present in these ordered phases, but the spin-charge separation/deconfinement serves as a driving force in the unconventional phase transitions of these ordered states to disordered states.
Magnetic Order and Superconductivity in the Bosonic t-J Model of CP1^11 Spinons and Doped Bosonic Holons
We study the three-dimensional U(1) lattice gauge theory of a CP1^11 spinon (Schwinger boson) field and a Higgs field. It is a bosonic ttt-JJJ model in slave-particle representation, describing the antiferromagnetic (AF) Heisenberg spin model with doped bosonic holes expressed by the Higgs field. The spinon coupling term of the action favors AF long-range order, whereas the holon hopping term in the ferromagnetic channel favors Bose-Einstein condensation (BEC) of holons. We investigate the phase structure by means of Monte-Carlo simulations and study an interplay of AF order and BEC of holes. We consider the two variations of the model; (i) the three-dimensional model at finite temperatures, and (ii) the two-dimensional model at vanishing temperature. In the model (i) we find that the AF order and BEC coexist at low temperatures and certain hole concentrations. In the model (ii), by varying the hole concentration and the stiffness of AF spin coupling, we find a phase diagram similar to the model (i). Implications of the results to systems of cold atoms and the fermionic ttt-JJJ model of strongly-correlated electrons are discussed.
Quantum phase transitions in d−waved-waved−wave superconductors
Based on an effective Lagrangian obtained from the holon-pair boson theory of Lee and Salk [Phys. Rev. B {\bf 64}, 052501 (2001)] for high TcT_cTc​ cuprates, we explore physical states involved with quantum phase transitions around a critical hole doping of d−waved-waved−wave superconductivity. We find a new quantum phase transition, a confinement to deconfinement transition for internal gauge charge in the superconducting phase. An antiferro- to para- magnetic transition in the superconducting state is explained in the context of the confinement to deconfinement transition. We obtain effective field theories in each region associated with the phase transitions.