We describe a solvable model of a quantum transition in a single band model involving a change in the size of the electron Fermi surface without any symmetry breaking. In a model with electron density $1-p$, we find a 'large' Fermi surface state with the conventional Luttinger volume $1-p$ of electrons for $p>p_c$, and a first order transition to a 'small' Fermi surface state with a non-Luttinger volume $p$ of holes for $p<p_c$. As required by extended Luttinger theorems, the small Fermi surface state also has fractionalized spinon excitations. The model has electrons with strong local interactions in a single band; after a canonical transformation, the interactions are transferred to a coupling to two layers of ancilla qubits, as proposed by Zhang and Sachdev (Phys. Rev. Research ${\bf 2}$, 023172 (2020)). Solvability is achieved by employing random exchange interactions within the ancilla layers, and taking the large $M$ limit with SU($M$) spin symmetry, as in the Sachdev-Ye-Kitaev models. The local electron spectral function of the small Fermi surface phase displays a particle-hole asymmetric pseudogap, and maps onto the spectral function of a lightly doped Kondo insulator of a Kondo-Heisenberg lattice model. We discuss connections to the physics of the hole-doped cuprates: the asymmetric pseudogap observed in STM, and the sudden change from incoherent to coherent anti-nodal spectra observed recently in photoemission. A holographic analogy to wormhole transitions between multiple black holes is briefly noted.
We propose a new parton theory of the hole-doped cuprates, describing the evolution from the pseudogap metal with small Fermi surfaces to the conventional Fermi liquid with a large Fermi surface. We introduce 2 ancilla qubits per square lattice site, and employ them to obtain a variational wavefunction of a fractionalized Fermi liquid for the pseudogap metal state. We propose a multi-layer Hamiltonion for the cuprates, with the electrons residing in the 'physical' layer, and the ancilla qubits in two 'hidden' layers: the hidden layers can be decoupled from the physical layer by a canonical tra…
We investigate the low-temperature behavior of Kondo lattices upon random depletion of the local $f$-moments, by using strong-coupling arguments and solving SU($N$) saddle-point equations on large lattices. For a large range of intermediate doping levels, between the coherent Fermi liquid of the dense lattice and the single-impurity Fermi liquid of the dilute limit, we find strongly inhomogeneous states that exhibit distinct non-Fermi liquid characteristics. In particular, the interplay of dopant disorder and strong interactions leads to rare weakly screened moments which dominate the bulk sus…
We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate …
We present details of the phase diagrams of fermionic systems with random and frustrated interactions, emphasizing the important role of the chemical potential. The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations, being controlled by quantum statistics. We compare the spin density diluted Sherrington-Kirkpatrick spin glass with classical spin 1 models such as the BEG model. We analyse in detail the infinite ra…
Fractionalized Fermi liquids and the cuprate phase diagram
Harvard University（哈佛大学）；California Institute of Technology（加州理工学院）；Flatiron Institute（平顿研究所）；Tata Institute of Fundamental Research（塔塔基础研究所）；The Abdus Salam International Centre for Theoretical Physics（阿卜杜斯·萨拉姆国际理论物理中心）
We show that fermion systems with random interactions lead to strong coupling of glassy order and fermionic correlations, which culminates in the implementation of Parisi replica permutation symmetry breaking (RPSB) in their T=0 quantum field theories. Precursor effects below fermionic AT-lines become stronger as the temperature decreases and play a crucial role within the entire low T regime. The Parisi ultrametric structure is shown to determine low energy excitations and the dynamic behaviour of fermionic correlations for large times, which is predicted to affect transport properties in met…
We propose a general theoretical framework, using two layers of ancilla qubits, for deconfined criticality between a Fermi liquid with a large Fermi surface, and a pseudogap metal with a small Fermi surface of electron-like quasiparticles. The pseudogap metal can be a magnetically ordered metal, or a fractionalized Fermi liquid (FL*) without magnetic order. A critical 'ghost' Fermi surface emerges (alongside the large electron Fermi surface) at the transition, with the ghost fermions carrying neither spin nor charge, but minimally coupled to $(U(1) \times U(1))/Z_2$ or $(SU(2) \times U(1))/Z_2…
Tractable model for a fractionalized Fermi liquid (FL$^*$) on a square lattice
Rutgers University（罗格斯大学）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Cornell University（康奈尔大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）
Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave (CDW)) order parameter, competing with superconductivity. We explicitly demonstrate the evolution from "Fermi arcs" (on the "large" Fermi surface) observed in ARPES experiments at relatively high temperatures (when both the amplitude and phase of density waves fluctuate randomly) towards formation…
We investigate parametrizations required to reproduce observed Fermi surfaces of overdoped and slightly underdoped LSCO in two different models. One is the standard three-band saddle-point slave boson (SB). The other is a model of CuO4 `molecules' randomly tiled in the plane, emphasizing the distinction between the local overlap, always the full (bare) one, and the effective overlap, connected with the reduced bandwidth due to the random tiling (RT). We conclude this distinction is physically significant for underdoped, but not for overdoped LSCO. This is consistent with the observed open Ferm…
The mesoscopic fluctuations of the Density of electronic States (DoS) and of the conductivity of two- and three- dimensional lattices with randomly distributed substitutional impurities are studied. Correlations of the levels lying above (or below) the Fermi surface, in addition to the correlations of the levels lying on opposite sides of the Fermi surface, take place at half filling due to nesting. The Bragg reflections mediate to increase static fluctuations of the conductivity in the middle of the band which change the distribution function of the conductivity at half- filling.
We analyze the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model, which describes complex fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. In a recent work [Phys. Rev. Research 2, 033084 (2020)] it has been shown that, upon varying filling or chemical potential, there exists a first-order quantum phase transition between a non-Fermi liquid (nFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low…
