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arXiv:cond-mat/0702119 · Physical Review B

Hole dynamics in an antiferromagnet across a deconfined quantum critical point

Ribhu K. Kaul, Alexei K. Kolezhuk, Michael Levin, Subir Sachdev A, T. Senthil

Published Jun 26, 2007• 64 citations
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Abstract

We study the effects of a small density of holes, $\ensuremath{\delta}$, on a square-lattice antiferromagnet undergoing a continuous transition from a N\'eel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero $\ensuremath{\delta}$, it is likely that the critical point broadens into a non-Fermi-liquid ``holon-metal'' phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio ${\mathrm{lim}}_{\ensuremath{\delta}\ensuremath{\rightarrow}0}{\mathcal{A}}_{F}∕\ensuremath{\delta}$ (where ${\mathcal{A}}_{F}$ is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at $\ensuremath{\delta}>0$, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as $\ensuremath{\delta}\ensuremath{\rightarrow}0$. We demonstrate that the electronic spectrum at the $\ensuremath{\delta}\ensuremath{\rightarrow}0$ transition is described by the ``boundary'' critical theory of an impurity coupled to a $(2+1)$-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble ``Fermi arc'' spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.

DOI
10.1103/physrevb.75.235122

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We study the effects of a small density of holes, \ensuremathδ\ensuremath{\delta}\ensuremathδ, on a square-lattice antiferromagnet undergoing a continuous transition from a N'eel state to a valence bond solid at a deconfined quantum critical point. We argue that at nonzero \ensuremathδ\ensuremath{\delta}\ensuremathδ, it is likely that the critical point broadens into a non-Fermi-liquid holon-metal'' phase with fractionalized excitations. The holon-metal phase is flanked on both sides by Fermi-liquid states with Fermi surfaces enclosing the usual Luttinger area. The electronic quasiparticles carry distinct quantum numbers in the two Fermi-liquid phases, and consequently we find that the ratio ${\mathrm{lim}}_{\ensuremath{\delta}\ensuremath{\rightarrow}0}{\mathcal{A}}_{F}∕\ensuremath{\delta}$ (where ${\mathcal{A}}_{F}$ is the area of a single hole pocket) has a factor of 2 discontinuity across the quantum critical point of the insulator. Note, however, that at $\ensuremath{\delta}>0$, there is no direct transition between these two Fermi-liquid states with distinct Fermi surface configurations; instead, there is an intermediate holon-metal phase whose width shrinks to zero as $\ensuremath{\delta}\ensuremath{\rightarrow}0$. We demonstrate that the electronic spectrum at the $\ensuremath{\delta}\ensuremath{\rightarrow}0$ transition is described by the boundary'' critical theory of an impurity coupled to a (2+1)(2+1)(2+1)-dimensional conformal field theory. We compute the finite temperature quantum critical electronic spectra and show that they resemble ``Fermi arc'' spectra seen in recent photoemission experiments on the pseudogap phase of the cuprates.
The quantum phase transitions of metals have been extensively studied in the rare-earth "heavy electron" materials, the cuprates, and related compounds. The Fermi surface of the metal often has different shapes in the states well away from the critical point. It has been proposed that these differences can persist up to the critical point, setting up a discontinuous Fermi surface change across a continuous quantum transition. We study square lattice antiferromagnets undergoing a continuous transition from a Neel state to a valence bond solid, and examine the fate of a small density of holes in the two phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both phases, enclosing the usual Luttinger area. However, additional quantum numbers cause the area enclosed by each Fermi surface pocket to jump by a factor of 2 across the transition in the limit of small density. We demonstrate that the electronic spectrum across this transition is described by a critical theory of a localized impurity coupled to a 2+1 dimensional conformal field theory. This critical theory also controls the more complex Fermi surface crossover at fixed density, which likely involves intermediate phases with exotic fractionalized excitations. We suggest that such theories control the electronic spectrum in the pseudogap phase of the cuprates.
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.
Deconfined quantum critical points have attracted lots of attention in the past decades but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for a new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids (FLs) in a bilayer model tuned by interlayer antiferromagnetic spin-spin coupling ${J}_{\ensuremath{\perp}}$. Across the transition the Fermi-surface volume per flavor jumps by 1/21/21/2 of the Brillouin zone, similar to the small to large Fermi-surface transitions in heavy fermion systems and maybe also in the high Tc{T}_{\text{c}}Tc​ cuprates. But in the bilayer case the small Fermi-surface phase (dubbed sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation discussed in high-energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to Higgs and/or confined phases of a $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$ gauge theory. We show that this deconfined FL to FL transition fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a composite of three deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined phase stable to zero temperature. Our work opens a direction to exploring deconfined metallic criticality and pairing mechanism from critical gauge field. The transition may be relevant to the recently found nickelate superconductor La3Ni2O7{\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}La3​Ni2​O7​ and future experiments in bilayer optical lattice.
We propose that quantum Hall bilayers in the presence of a periodic potential at the scale of the magnetic length can host examples of a deconfined metal-insulator transition (DMIT), where a Fermi-liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or an insulator with Goldstone modes) through a continuous quantum phase transition.The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework.At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL).The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different.The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles.Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase.We discuss the topological properties of the insulator and various observable signatures associated with the DMIT.
We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction between any pair of sites and a constraint of no double occupancy.A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a nonzero critical value p c of the hole doping p away from the half-filled insulator.We compute the renormalization group to two loops, but some exponents are obtained to all loop order.We argue that the critical point p c is flanked by confining phases: a disordered Fermi liquid with carrier density 1 þ p for p > p c and a metallic spin glass with carrier density p for p < p c .Additional evidence for the critical behavior is obtained from a large-M analysis of a model which extends the SU(2) spin symmetry to SUðMÞ.We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.
States with gapless degrees of freedom are typically more complicated and less well- understood than systems possessing a gap. In this thesis, we study strongly-correlated systems described by gapless fermions. In most of the systems we consider, the fermionic excitations are emergent, i.e. they are not adiabatically connected to the electrons which constitute the fundamental building blocks of the system in question.\nWe start by proposing several novel states of matter which we claim are relevant to strongly-correlated systems. The rst state we present is a fractionalized Fermi liquid on the surface of a topological Kondo insulator. A Kondo insulator is a material which becomes insulating at low temperatures as a result of strong electron-spin interactions. When spin- orbit coupling is present, this insulator might be topological and, consequently, host robust gapless surface modes. Given the strong interactions and the decreased dimensionality of the surface, we propose that the spins and electrons there may decouple, resulting in the formation of a fractionalized Fermi liquid.\nWe next argue that quantum electrodynamics in 2+1 dimensions (QED3) with Nf = 4 fermion avours may describe a continuous, decon ned phase transition connecting the 120◦ coplanar Néel phase and the √12 × √12 valence bond solid phase of the triangular lattice antiferromagnet (AF). In addition to being a critical point, QED3 is also believed to describe a critical phase of matter called the Dirac spin liquid. Regardless of whether QED3 is manifest as a phase or a critical point, impurities and imperfections are always present in the real world, and it is therefore important to understand what e ects this may have. We show that when QED3 is perturbed by weak disorder, under certain circumstances, it ows to a new critical point in which both interactions and disorder are present.\nConclusively identifying a system described by QED3 has proven to be a di cult task, not only experimentally, but in numerical studies as well. Since QED3 is a critical theory, its spectrum on a torus is a universal quantity dependent only on low-energy degrees of freedom, such as the torus area. It follows that this data is accessible via exact diagonalization and can serve as an identifying signature of the theory. To this end, we calculate the QED3 torus spectrum using path integral methods.\nWe conclude this thesis with a comprehensive study of gapped Z2 spin liquids of the square lattice antiferrogmagnet, using a critical theory of Dirac fermions coupled to an SU(2) gauge eld as a starting point. There are many di erent Z2 spin liquid groundstates which preserve the same symmetry group. Even if one knows that a system has a Z2 spin liquid groundstate, it is by no means obvious which Z2 spin liquid is being realized. By starting from a gapless theory, the set of possibilities can be reduce considerably. Further, using certain recently proposed dualities, comparisons with theories formulated using bosons can be made.