We study the consequences of disorder in the Kitaev honeycomb model, considering both site dilution and exchange randomness. We show that a single vacancy binds a flux and induces a local moment. This moment is polarised by an applied field $h$: in the gapless phase, for small $h$ the local susceptibility diverges as $χ(h)\sim\ln(1/h)$; for a pair of nearby vacancies on the same sublattice, this even increases to $χ(h)\sim1/(h[\ln(1/h)]^{3/2})$. By contrast, weak exchange randomness does not qualitatively alter the susceptibility but has its signature in the heat capacity, which in the gapless phase is power law in temperature with an exponent dependent on disorder strength.
We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. We find that the transition is signaled by a sharp increase in the sensitivity of a suitably averaged entanglement entropy with respect to disorder -- the magnitude of its disorder derivative appears to diverge in the thermodynamic limit. We also study the level statistics of the entanglement spectrum as a function of disorder. However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction…
We provide strong evidence of a quantum critical point (QCP) associated with the destruction of Kondo screening in the Anderson-Hubbard model for interacting electrons with quenched disorder. A unique crossover energy scale, $ω^*$ separating the Fermi liquid and non-Fermi liquid (nFL) scattering dynamics on the metallic side of the quantum critical fan is identified. The scale vanishes at the disorder driven QCP. We interpret our results by measuring the distribution of Kondo scales and find that the QCP occurs when this distribution acquires a finite intercept, indicating a Kondo destruction …
The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. However, deviations from the original Kitaev model are expected to appear in real materials. In this Letter, we investigate the fate of Kitaev's spin liquid in the presence of disorder -- bond defects or vacancies -- for an extended version of the model. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a nonuniversal exponent. We link this power-law distribution of energy scales to weakly coup…
An analytical solution of the Mott transition is obtained for the Hubbard model on the Bethe lattice in the large coordination number ($z$) limit. The excitonic binding of doublons (doubly occupied sites) and holons (empty sites) is shown to be the origin of a continuous Mott transition between a metal and an emergent quantum spin liquid insulator. The doublon-holon binding theory enables a different large-$z$ limit and a different phase structure than the dynamical meanfield theory by allowing intersite spinon correlations to lift the $2^N$-fold degeneracy of the local moments in the insulati…
We present a detailed study of the ground-state entanglement in disordered fractional quantum Hall liquids. We consider electrons at various filling fractions $f$ in the lowest Landau level, with Coulomb interactions. At $f=1/3,1/5$ and $2/5$ where an incompressible ground-state manifold exists at zero disorder, we observe a pronounced minimum in the derivative of entanglement entropy with respect to disorder. At each filling, the position of this minimum is stable against increasing system size, but its magnitude grows monotonically and appears to diverge in the thermodynamic limit. We consid…
We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interacti…
We calculate analytically the low temperature quasi-particle scattering rate, the conductivity, and the specific heat in weakly disordered metals close to a quantum critical point, via the use of a proper fluctuation potential $V(q,ω)$ between the quasi-particles. We obtain typical Fermi liquid results proportional to $T^2$ and $T$ respectively, with prefactors which diverge as power laws of the control parameter $a$ upon approaching the critical point. The Kadowaki-Woods ratio is shown to be independent of $a$ (possibly times a logarithmic dependence on $a$) only for the case of three-dimensi…
The stability of the Dirac spin-liquid on two-dimensional lattices has long been debated. It was recently demonstrated [Nature Commun. 10, 4254 (2019) and Phys. Rev. B 93, 144411 (2016)] that the staggered $π$-flux Dirac spin-liquid phase on the non-bipartite triangular lattice may be stable in the clean limit. However, quenched disorder plays a crucial role in determining whether such a phase is experimentally viable. For SU(2) spin systems, the effective zero-temperature, low-energy description of Dirac spin-liquids in $(2+1)$ dimensions is given by the compact quantum electrodynamics ($\rm …
The interplay of interactions and disorder in two-dimensional (2D) electron systems has actively been studied for decades. The paradigmatic approach involves starting with a clean Fermi liquid and perturbing the system with both disorder and interactions. We instead start with a clean non-Fermi liquid near a 2D ferromagnetic quantum critical point and consider the effects of disorder. In contrast with the disordered Fermi liquid, we find that our model does not suffer from runaway flows to strong coupling and the system has a marginally stable fixed point with perfect conduction.
We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $ε$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak…
We study a class of disordered continuous classical spin systems including the kagome Heisenberg magnet. While each term in its local Hamiltonian can be independently minimised, we find {\it discrete} degenerate ground states whose number grows exponentially with system size. These states do not exhibit zero-energy `excitations' characteristic of highly frustrated magnets but instead are local minima of the energy landscape, albeit with an anomalously soft excitation spectrum. This represents a spin liquid version of the phenomenon of jamming familiar from granular media and structural glasses…
We suggest that a randomization of the pseudo-dipolar interaction in the spin-orbit-generated low-energy Hamiltonian of YbMgGaO$_4$ due to an inhomogeneous charge environment from a natural mixing of Mg$^{2+}$ and Ga$^{3+}$ can give rise to orientational spin disorder and mimic a spin-liquid-like state. In the absence of such quenched disorder, $1/S$ and density matrix renormalization group calculations both show robust ordered states for the physically relevant phases of the model. Our scenario is consistent with the available experimental data and further experiments are proposed to support …
We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number $N$ of fermions are obtained and …
We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with increasing disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic L…
The interplay between geometric frustration (GF) and bond disorder is studied in the Ising kagome lattice within a cluster approach. The model considers antiferromagnetic (AF) short-range couplings and long-range intercluster disordered interactions. The replica formalism is used to obtain an effective single cluster model from where the thermodynamics is analyzed by exact diagonalization. We found that the presence of GF can introduce cluster freezing at very low levels of disorder. The system exhibits an entropy plateau followed by a large entropy drop close to the freezing temperature. In t…
The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. In the pyrochlore Tb$_2$Hf$_2$O$_7$, we demonstrate that the vicinity of the disordering transition towards a defective fluorite structure translate…
We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals, which exhibit birefringent spectra in the absence of interactions. Coulomb interactions drive the system to a marginal Fermi liquid, both for the two-dimensional (2d) and three-dimensional (3d) cases. Short-ranged correlated disorder in 2d, or a power-law correlated disorder 3d, has the same engineering dimension as the Coulomb term, in a renormalization group (RG) sense. In order to analyze the combined effects of these two kinds of interactions, we apply a dimensional regularization sch…
We consider a two-dimensional disordered conductor in the regime when the superconducting phase is destroyed by the magnetic field. We analyze a combination of fluctuations of different origin which results in an effective interaction amplitude suitable for a spontaneous s-wave odd-frequency pairing instability. We observe that the end point of the superconductivity is a quantum critical point separating the conventional superconducting phase from a state with the odd-frequency spin-triplet pairing instability. We speculate that this could shed light on a rather mysterious insulating state obs…
The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter- and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out…
We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focussing on the behaviour of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area/volume law entanglement, being characteristic of the quantum disentangled liquid. This behaviour appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding…
In recent years, several magnetic Mott insulators with strong spin-orbit couplings were suggested to be proximate to the Kitaev quantum spin liquid (QSL) whose one of the most exciting features is the fractionalization of spin excitations into itinerant Majorana fermions and static $Z_2$ fluxes. Motivated by the emergence of this plethora of 4d and 5d transition metal Kitaev materials and by the fact that some level of disorder is inevitable in real materials, here we study how the Kitaev QSL responds to various forms of disorder, such as vacancies, impurities, and bond randomness. First, we a…
Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs - pyrochlore magnets based on non-Kramers ions such as Pr$^{3+}$ or Tb$^{3+}$- structural disorder can …
Disordered electron liquid in double quantum well heterostructures: Renormalization group analysis and dephasing rate
我们报告了电子-电子相互作用对物理观测量（电导等）的影响的详细研究。双量子阱异质结构中的无序电子液体。我们发现，即使在两个量子阱中的电子的共同弹性散射的情况下，在量子阱中的电子-电子相互作用的不对称性和内部在低温下使他们困惑。我们的研究结果与最近的量子阱Al $_x$ Ga $_{1-x}$ As/GaAs/Al $_x$ Ga $_{1-x}$ As异质结的输运实验定量一致。
