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arXiv:0912.1684

Non-Fermi liquid from confinement in doped Mott insulators

Ki‐Seok Kim, Hyun-Chul Kim

Published Dec 9, 2009• 0 citations
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Abstract

A phenomenological description for confinement of fractionalized excitations is proposed in the gauge theory approach for doped Mott insulators. Introducing the Polyakov-loop parameter into an SU(2) gauge theory for the t-J model, we show that electron excitations emerge below the so-called coherence temperature, resulting from confinement of spinons and holons via the formation of the Polyakov loop. Remarkably, such confined electrons turn out to exhibit non-Fermi liquid physics without quantum criticality, yielding the electric resistivity in quantitative agreement with experimental data. The Higgs phase is not allowed due to confinement, suggesting a possible novel mechanism of superconductivity in the strong coupling approach.

DOI
10.48550/arxiv.0912.1684

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A phenomenological description for confinement of fractionalized excitations is proposed in the gauge theory approach for doped Mott insulators. Introducing the Polyakov-loop parameter into an SU(2) gauge theory for the t-J model, we show that electron excitations emerge below the so-called coherence temperature, resulting from confinement of spinons and holons via the formation of the Polyakov loop. Remarkably, such confined electrons turn out to exhibit non-Fermi liquid physics without quantum criticality, yielding the electric resistivity in quantitative agreement with experimental data. The Higgs phase is not allowed due to confinement, suggesting a possible novel mechanism of superconductivity in the strong coupling approach.
Marginal Fermi-liquid physics near optimal doping in high T(c) cuprates has been explained within two competing scenarios such as the spin-fluctuation theory based on an itinerant picture and the slave-particle approach based on a localized picture. In this study we propose an alternative scenario for the anomalous transport within the context of the slave-particle approach. Although the marginal Fermi-liquid phenomenology was interpreted previously within deconfinement of the compact gauge theory, referred to as the strange metal phase, we start from confinement, introducing the Polyakov loop parameter into an SU(2) gauge theory formulation of the t-J model. The Polyakov loop parameter gives rise to incoherent electrons through the confinement of spinons and holons, which result from huge imaginary parts of self-energy corrections for spinons and holons. This confinement scenario serves a novel mechanism for the marginal Fermi-liquid transport in the respect that the scattering source has nothing to do with symmetry breaking. Furthermore, the incoherent Fermi-liquid state evolves into the Fermi-liquid phase through crossover instead of an artificial second-order transition as temperature is lowered, where the crossover phenomenon does not result from the Anderson-Higgs mechanism but originates from an energy scale in the holon sector. We fit experimental data for the electrical resistivity around the optimal doping and find a reasonable match between our theory and the experiment.
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.
Electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, charge transport is governed by chiral spinon excitation, comprising a bosonic spin-12\frac{1}{2}21​ at the core of a supercurrent vortex. It leads to vanishing resistivity with the confinement of the spinons in the superconducting phase but low-TTT divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number nH={n}_{H}=nH​= doping concentration $\ensuremath{\delta}$ and a Nernst effect to signal underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit linear-TTT resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom.
Abstract The phenomenon of Mott insulation involves the localisation of itinerant electrons due to strong local repulsion. Upon doping, a pseudogap (PG) phase emerges—marked by selective gapping of the Fermi surface without conventional symmetry breaking in spin or charge channels. A key challenge is understanding how quasiparticle breakdown in the Fermi liquid (FL) gives rise to this enigmatic state, and how it connects to both the Mott insulating and superconducting phases. Here, we develop a renormalisation-based construction of strongly correlated lattice models that captures the emergence of the PG phase and its transition to a Mott insulator. Applying a many-body tiling scheme to the fixed-point impurity model uncovers a lattice model with electron interactions and Kondo physics. At half-filling, the interplay between Kondo screening and bath charge fluctuations in the impurity model leads to FL breakdown. This reveals a PG phase characterised by a non-FL (the Mott metal) residing on nodal arcs, gapped antinodal regions of the Fermi surface, and an anomalous scaling of the electronic scattering rate with frequency. The eventual confinement of holon–doublon excitations of this exotic metal obtains a continuous transition into the Mott insulator. Our results identify the PG as a distinct long-range entangled quantum phase, and offer a new route to Mott criticality beyond the paradigm of local quantum criticality.
We present a quantum field theoretic description on the t – J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern–Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t – J model. Finally, a finite-temperature phase diagram is proposed. The metal–insulator transition observed in in-plane resistivity measurement is identified to a confinement–deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter “Polyakov-line”.
We propose one possible mechanism for an anomalous metallic phase appearing frequently in two spatial dimensions, that is, local pairing fluctuations. Introducing a pair-rotor representation to decompose bare electrons into collective pairing excitations and renormalized electrons, we derive an SU(2) gauge theory of the Hubbard model as an extended version of its U(1) gauge theory. Since our effective SU(2) gauge theory admits two kinds of collective bosons corresponding to pair excitations and density fluctuations, respectively, an intermediate phase appears naturally between the spin liquid Mott insulator and Fermi liquid metal of the U(1) gauge theory, characterized by softening of density-fluctuation modes as the Fermi liquid, but gapping of pair-excitation modes. We show that this intermediate phase is identified with an anomalous metallic phase because there are no electronlike quasiparticles although it is metallic.