Session F50: Non-Fermi Liquids

Two-dimensional non-Fermi liquids with quenched disorder

Despite significant theoretical progress, the effect of quenched disorder on non-Fermi liquids with a finite density of fermions interacting with soft order parameter fluctuations near a quantum critical point remains poorly understood. We study the interplay of disorder and interactions in the exactly solvable "matrix large N" non-Fermi liquid model in two spatial dimensions. We investigate the stability of the corresponding strongly interacting fixed point and show that diffusive effects drastically modify the properties of the critical regime and associated critical exponents.
  

Pairing Instability on a Luttinger Surface: A Non-Fermi Liquid to Superconductor Transition and its SYK Dual

Instabilities of the Fermi Surface -- contours of poles of the single particle Green function -- such as superconductivity, density waves (CDW, SDW, PDW..) etc are now a commonplace in modern condensed matter physics. In this talk, I will discuss the problem of superconducting instability on a model Luttinger surface, or contours of zeros of the many-body Green function.

Unlike a Fermi surface, in the presence of an attractive potential, the model exhibits -- in the strong coupling limit -- a quantum phase transition into a superconducting state. The spectral density of pair fluctuations in the "normal" state of the superconductor has a power-law type van-Hove singularity signalling non-Fermi liquid transport. Crucially, the fluctuation free energy in the non-Fermi liquid resembles well-studied models with gravity duals such as SYK. These results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mottness and strongly coupled toy-models exhibiting gravity duals.   

Low-energy level spacing and entropy change across SYK non-Fermi liquid to a Fermi Liquid transition for finite-N

We study a quantum phase transition (QPT) between a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) and a Fermi liquid in a solvable large-N model where the zero-temperature residual entropy of the NFL vanishes continuously at the QPT in the large-N limit. We show via exact diagonalization that, even at finite-N, the QPT manifests itself in the system-size scaling of low-energy level spacings above the ground state. The evidence of this QPT is also directly visible in the single-particle Greens function and, indirectly, in the thermalization dynamics after a quench. Interestingly, we find that the QPT has little effect on the entanglement entropy in the ground state. We also construct the effective low-energy field theory across the QPT by considering fluctuations around the large-N limit.   

Phases of the t-J model with random and all-to-all hopping and exchange

We study a t-J model with both t and J random and all-to-all. This model has been studied earlier [1], and can be mapped to an Anderson impurity coupled to self-consistent fermionic and bosonic baths. We employ renormalization group and large M (for models with SU(M) spin symmetry) analyses, and find evidence for a critical non-Fermi liquid phase at zero temperature and small doping. The critical spin correlations are similar to those in a random magnet [2]. A disordered Fermi liquid phase is expected at large doping. We note connections to the physics of the underdoped cuprates.

[1] O. Parcollet and A. Georges, Physical Review B 59, 5341 (1999).
[2] S. Sachdev and J. Ye, Physical Review Letters 70, 3339 (1993).   

Fermi-surface Reconstruction in the Repulsive Fermi-Hubbard Model

One of the fundamental questions about the high temperature cuprate superconductors is the size of the Fermi surface underlying the superconducting state. By analyzing the single particle spectral function for the Fermi Hubbard model as a function of repulsion U and chemical potential μ, we find that the Fermi surface reconstructs from a large Fermi surface enclosing (1+p) holes, matching the Luttinger volume as expected in a Fermi liquid, to a small Fermi surface enclosing only p holes, thereby transitioning into a non-Fermi liquid FL* phase, as the Mott insulator at half filling is approached. We obtain the Fermi surface contour by combining results of: (a) momentum distribution function n_k = 1/2, (b) spectral weight A_k(ω = 0), and (c) retarded Green's function, G_k^ret(E) = 0, calculated using determinantal quantum Monte Carlo and analytic continuation methods. We compare our numerical results with experiments on Hall measurements.
  

Probing out-of-time-order correlators using thermofield double states

We propose a new family of protocols for measurements of out-of-time order correlators (OTOCs) that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of a quantum system. In particular, we show how Lyapunov exponents of quantum chaotic systems can be extracted from various time-ordered correlators (including equilibrium Green’s functions) in the TFD state. Importantly, TFD states can be realized as ground states of simple Hamiltonians coupling two identical systems, which underlies their usefulness for experimental explorations of quantum chaos. We numerically test our protocols on two coupled SYK models, recently proposed to be dual to an eternal traversable wormhole, and discuss possible realizations of this setup.   

Non-Laudau Quantum Phase Transitions and Nearly-Marginal Fermi Liquid

Marginal fermi liquid and quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, which could occur in strongly interacting quantum many-body systems. This work demonstrates that these two phenomena may be tightly connected. To elaborate this connection, we propose a physical mechanism for "nearly-marginal Fermi liquid", namely the fermion self-energy scales as Σ_f(iω)~i sgn(ω)|ω|^α with α close to 1 in a considerable energy window. The nearly-marginal fermi liquid is obtained by coupling an electron fermi surface to unconventional QCPs that are beyond the Landau's paradigm. This mechanism relies on the observation that the anomalous dimension η of the order parameter of these unconventional QCPs can be close to 1, which is significantly larger than conventional Laudau phase transitions. The fact that η~1 justifies a controlled perturbative renormalization group expansion proposed previously. Candidate QCPs that meet this desired condition are proposed.   

Planckian superconductor

The Planckian relaxation rate h/t_P=2πk_BT sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. We show that at the critical coupling between a superconducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap Δ behaves as η h/t_P at low temperatures, where η is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite Δ domain is settled between the two critical temperatures   

Branching time and Many-body Chaos

Branching time is defined in terms of the retarded kernel to quantify the stringy effects in SYK-like models. In this work, after presenting a weighting trick to calculate the branching time, we prove a bound on the branching time for a large class of systems. We also derive a relation between the branching time, the Lyapunov exponent and the quasiparticle lifetime for weakly coupling models.   

A cascade of non-Fermi liquid crossovers from an interplay of local and bosonic quantum criticality

We present examples of multi-orbital electronic lattice models, coupled to bosonic collective modes with modified Sachdev-Ye-Kitaev form of interactions, which become solvable when the number of orbitals and collective modes is taken to be large. At high energies, these models display non-Fermi liquid behavior with local quantum criticality and are described by a strongly coupled electron-boson fluid. As a function of decreasing energy scales, they exhibit a crossover into an incipient heavy Fermi liquid regime, where the interaction between the bosonic mode and the coherent electronic quasiparticles near the Fermi surface leads to Landau damping. When the boson gap is tuned to criticality, the feedback of the damped boson on the electrons leads to a low-temperature non-Fermi liquid with a critical Fermi surface. Our models thus describe a cascade of crossovers from a dynamical critical exponent z=∞ down to z=3 in a controlled setting as a function of decreasing energy scales.   

Bose Metal as a Nematic Phase Glass

A widely accepted microscopic theory for the Bose metal has yet to emerge despite mounting experimental evidence of a metallic phase intervening between the extremes of superfluid and insulator for low-temperature bosons. The reasons for this are two-fold: metallic solutions tend to be highly unstable, and stable solutions tend to utilize the unphysical limit of arbitrarily low particle density. We present a first-of-its-kind stable microscopic theory for the Bose metal with constant particle density in the thermodynamic limit. In this theory, repulsive interactions cause spontaneous symmetry breaking in an otherwise massively degenerate single-particle ground state. The key physics behind the stability of the Bose metal lies in the structure of the phase coherence. In contrast to the typical isotropic long-range order of superfluidity, our 3D theory exhibits long-range nematic phase coherence in each 2D plane while suffering from short range decoherence between planes. The resulting current response cannot maintain phase coherence beyond a finite length scale. Our discovery of a stable low-temperature phase that exhibits metallic conductivity elevates the Bose metal to one of the fundamentally intrinsic bosonic phases of matter alongside that of the superfluid and insulator.   

Exploring order-to-order transitions of Dirac fermions in the regime of strong interactions

In recent years, there has been a growing interest in direct and continuous quantum phase transitions between ordered phases that do not conform with the Landau-Ginzburg paradigm. It has since been a challenge to identify models that host such transitions.
One model of interest consists of interacting Dirac fermions coupled to a transverse-field Ising model on the honeycomb lattice. It has been suggested that there is an order-to-order transition between the competing antiferromagnetic (AFM) and Ising ordered phases of this model [1].
However, the quantum Monte Carlo simulations employed were restricted to relatively small system sizes so that finite-size effects remain an issue. In the strongly interacting regime, this system can be described by an effective quantum spin model of coupled Heisenberg and Ising spins.
Within this setting, highly efficient quantum Monte Carlo methods available for spin systems can be used to drastically improve on the precision of the original fermionic estimates. In our simulations, we resolve a narrow coexistence region between the Ising and AFM-ordered phases, in contrast to the direct single transition proposed in Ref. [1].

[1] T. Sato, M. Hohenadler, and Fakher F. Assaad, PRL 119, 197203(2017)   

Scale Invariant Entanglement Negativity at the Many-Body Localization Transition

The exact nature of the many-body localization transition remains an open question. An aspect which has been posited in various studies is the emergence of scale invariance around this point, however the direct observation of this phenomenon is still absent. Here we achieve this by studying the logarithmic negativity and mutual information between disjoint blocks of varying size across the many-body localization transition. The two length scales, block sizes and the distance between them, provide a clear quantitative probe of scale invariance across different length scales. We find that at the transition point, the logarithmic negativity obeys a scale invariant exponential decay with respect to the ratio of block separation to size, whereas the mutual information obeys a polynomial decay. The observed scale invariance of the quantum correlations in a microscopic model opens the direction to probe the fractal structure in critical eigenstates using tensor network techniques and provide constraints on the theory of the many-body localization transition.   

g=2 nonlinear sigma model revisited

We consider the transport properties of free fermions with gyromagnetic ratio g=2 in the presence of quenched disorder. This system has been shown to be closely related to the mean-field limit of various composite fermion theories [1,2,3]. We derive the nonlinear sigma model that describes the electrical and spin conductivities via the supersymmetric approach [4], and discuss its physical implications for various quantum phase transitions.

[1] Phys. Rev.B 98 (11) , 115105
[2] Phys. Rev.B 99 (23) , 235114
[3] ArXiv:1907.13141
[4] Adv. Phys. 32, 53 (1983)