Fractionalized Fermi Liquids

Abstract

In spatial dimensions d ≥ 2, Kondo lattice models of conduction and local moment electrons can exhibit a fractionalized, non-magnetic state (FL * ) with a Fermi surface of sharp electron-like quasiparticles, enclosing a volume quantized by (ρa − 1)(mod 2), with ρa the mean number of all electrons per unit cell of the ground state. Such states have fractionalized excitations linked to the deconfined phase of a gauge theory. Confinement leads to a conventional Fermi liquid state, with a Fermi volume quantized by ρa(mod 2), and an intermediate superconducting state for the Z2 gauge case. The FL * state permits a second order metamagnetic transition in an applied magnetic field.The physics of the heavy fermion metals, intermetallic compounds containing localized spin moments on d or f orbitals and additional bands of conduction electrons, has been of central interest in the theory of correlated electron systems for several decades [1][2][3]. These systems are conveniently modelled by the much studied Kondo lattice Hamiltonian, in which there are exchange interactions between the local moments and the conduction electrons, and possibly additional exchange couplings between the local moments themselves. To be specific, one popular Hamiltonian to which our results apply is:Here the local moments are S = 1/2 spin S j , and the conduction electrons c jσ (σ =↑↓) hop on the sites j, j ′ of some regular lattice in d spatial dimensions with amplitude t(j, j ′ ), J K > 0 are the Kondo exchanges ( τ are the Pauli matrices), and explicit short-range Heisenberg exchanges, J H , between the local moments have been introduced for theoretical convenience. A chemical potential for the c σ fermions which fixes their mean number at ρ c per unit cell of the ground state is implied. We have not included any direct couplings between the conduction electrons as these are assumed to be well accounted by innocuous Fermi liquid renormalizations. For simplicity, we restrict our attention here to nonmagnetic states, in which there is no average static moment on any site ( S j = 0), and the spin rotation invariance of the Hamiltonian is preserved: the S j moments have been 'screened', either by the c σ conduction electrons, or by their mutual interactions (there is a natural extension of our results to magnetic states). It is widely accepted [1,[3][4][5][6][7] that such a ground state of H is a conventional Fermi liquid (FL) with a Fermi surface of 'heavy' quasiparticles, enclosing a volume, V F L determined by the Luttinger theorem:Hereis a phase space factor, v 0 is the volume of the unit cell of the ground state, ρ a = n ℓ + ρ c is the mean number of all electrons per volume v 0 , and n ℓ (an integer) is the number of local moments per volume v 0 . Note that ρ c,a need not be integers, and the (mod 2) in (2) allows neglect of fully filled bands. In d = 1, (2) has been established rigorously by Yamanaka et al. [5]. In general d, a non-perturbative argument for (2), assuming that the ground state is a Fermi liquid, has been provided by Oshikaw...

Understanding correlated electron systems by a classification of Mott insulators

“…It has been argued recently [34,35] that a different possibility is more likely for the doped RVB Mott insulator in d ≥ 2 spatial dimensions. The doped electrons (or holes), instead of fractionalizing into spinless charged particles and neutral S = 1/2 spinons, retain their integrity in the ground state, and their spin and charge remain bound to each other.…”

Fermi surface reconstruction in hole-dopedt−Jmodels without long-range antiferromagnetic order

“…Such ground states realize a fractionalized Fermi liquid. 13,14 Our starting point is the spinon-dopon formulation of the t-J model developed by Ribeiro and Wen. 20 In this representation the elementary excitations are spinons, which carry spin-1/2 but no charge, and dopons, which carry spin-1/2 and charge.…”

“…10,11 In fact, many of the unresolved theoretical problems in strongly correlated electron materials, from heavy-Fermion compounds to high-T c cuprates, are related to the fate of electronic excitations close to antiferromagnetic quantum critical points. 12 It has been been argued, however, that the critical point between a metal with a large Fermi surface and an antiferromagnetic metal with small Fermi pockets may be replaced by a new intermediate phase, the so called fractionalized Fermi liquid (FL*) 13,14 , which exhibits small pockets similar to the antiferromagnetic metal, but breaks no symmetries: summaries of these arguments, and of previous theoretical work, can be found in two recent reviews. 15,16 The simplest picture of the FL* phase appears in the context of Kondo lattice models coupling a lattice of localized f moments and a conduction band of itinerant c electrons.…”

“…Then the f moments may form a spin liquid, which does not break any symmetries of the lattice Hamiltonian. The formation of the spin liquid also quenches the Kondo effect, and so the effective value of J K does not renormalize to infinity as it does in the single impurity Kondo model 13,14,17 . The c electrons are now only weakly coupled to the f spin liquid, and so the c electrons form a "small" Fermi surface which encloses a volume controlled only by the density of c electrons, which violates the traditional Luttinger count.…”

Localized moments and the stability of antiferromagnetic order in Yb3Pt4

“…Initially, it was thought that the unusual divergencies of the specific heat and magnetic susceptibilities that were found near QCPs, as well as electrical resistivities with linear temperature dependencies, phenomena collectively referred to as 'non-Fermi liquid' behavior, reflected the dominance of quantum critical fluctuations. However, it has become clear that in at least a few cases, that the QCP affects the electronic structure itself, where T = 0 electronic delocalization leads to a change in the Fermi surface volume at or near the QCP [7][8][9] . Evidence for these Fermi surface volume changes come from Hall effect measurements near the field-driven QCP in YbRh 2 Si 2 10-12 , from discontinuous changes in quantum oscillations and moment localization near the pressure -driven QCP in CeRhIn 5 13,14 , and from the values of the quantum critical exponents themselves 8,15 .…”