Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Q63: Unconventional Quantum LiquidsRecordings Available

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Sponsoring Units: DCMP Chair: Yuxuan Wang, Univ. of Florida Room: Hyatt Regency Hotel Grant Park A 
Wednesday, March 16, 2022 3:00PM  3:12PM 
Q63.00001: Finite temperature corrections to chaotic models in and out of equilibrium Yuri D Lensky There has been a renewed interest in chaotic quantum models, motivated by developments in both condensed matter and quantum gravity, as well as the introduction of the now paradigmatic solvable example, the SachdevYeKitaev (SYK) ensemble. The low temperature limits of this model and its generalizations have provided key insight into the behaviour of strongly coupled quantum systems, and have served as quantitative proofs of concept for protocols to probe and control them. The understanding of these effects is informed by a dual gravitational description, which has inspired generalizations with surprising properties such as recurrences and arresting thermalization with a drive. By going beyond the low temperature limit in these models in and out of equilibrium, we show that high temperature corrections actually have important qualitative effects that persist in the low temperature limit. We discuss how the dual description has to be modified and the consequences of these modifications to the physics of SYKlike models. 
Wednesday, March 16, 2022 3:12PM  3:24PM 
Q63.00002: Solvable model for a charge4e superconductor Nikolay Gnezdilov, Yuxuan Wang A charge4e superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge4e superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the meanfield level. We propose a solvable model for a charge4e superconductor  a spinful version of the SachdevYeKitaev model with an extra quartic anomalous term. Despite explicit violation of particle number conservation, the model remains gapless and satisfies Luttinger's theorem. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge4e order parameter, in sharp contrast with a regular (charge2e) superconductor. Upon lowering temperature, we show that the correlation between charge4e order and regular interaction terms can drive a firstorder phase transition to a charge2e superconducting state. 
Wednesday, March 16, 2022 3:24PM  3:36PM 
Q63.00003: Superconductivity of incoherent electrons in YukawaSYK model Laura Classen, Andrey V Chubukov We explore the interplay between nonFermi liquid and superconductivity in a strongly coupled, quantumcritical environment within a model of N fermions in a quantum dot coupled to M bosons by a disorderinduced complex Yukawa coupling (YukawaSYK model). We analyze the phase diagram for an arbitrary interaction and ratio of N/M with special focus on two nonFermiliquid regimes: an SYKlike regime with a powerlaw frequency dependence of the fermionic selfenergy and an impuritylike regime with frequency independent selfenergy. We show that the crossover between the two can be reached by varying either the strength of the fermionboson coupling or the ratio M/N. In both regimes, the system is unstable to superconductivity if the strength of timereversalsymmetrybreaking disorder is below a certain threshold, and we determine the behavior of the corresponding onset temperatures. We argue that the superconducting state is highly unconventional with an infinite set of minima of the condensation energy at T=0 corresponding to topologically different gap functions. We discuss similarities and differences between this model and the $\gamma$model, which describes dispersionfull fermions tuned to a metallic quantumcritical point with an effective singular dynamical interaction. 
Wednesday, March 16, 2022 3:36PM  3:48PM 
Q63.00004: Strong correlation effects in SNS junctions and failed superconductors Akshat Pandey, Steven A Kivelson, Boris Spivak A wide variety of well characterized experimental systems exhibit anomalous metallic states in which current is carried by large superconducting quantum fluctuations that remain uncondensed to the lowest accessible temperatures. As a first step toward a theory of such a state, we revisit the case of a single SNS junction, but taking into account interaction effects in the normal metal portion of the junction. In particular, we identify circumstances in which magnetic fluctuations lead to dynamical variations in the sign of the Josephson coupling  i.e. in the sign of the local superfluid density. This has important implications for the theory of the anomalous metal more generally. 
Wednesday, March 16, 2022 3:48PM  4:00PM 
Q63.00005: Spin liquid to spin glass crossover in the random quantum Heisenberg magnet Subir Sachdev, Maine Christos, Felix M Haehl We study quantum SU(M) spins with alltoall and random Heisenberg exchange interactions of rootmeansquare strength J. The large M model has a spin liquid ground state with the spinons obeying the equations of the SachdevYeKitaev (SYK) model. Numerical studies of the SU(2) model with S=1/2 spins show spin glass order in the ground state, but also display SYK spin liquid behavior in the intermediate frequency spin spectrum. We employ a 1/M expansion to describe the crossover from fractionalized fermionic spinons to a confining spin glass state with weak spin glass order q_{EA}. The SYK spin liquid behavior persists down to a frequency ω_{s }∼ Jq_{EA}, and for ω < ω_{s}, the spectral density is linear in ω, thus quenching the extensive zero temperature entropy of the spin liquid. The linear ω spectrum is qualitatively similar to that obtained earlier using bosonic spinons for large q_{EA}. We argue that the extensive SYK spin liquid entropy is transformed as T→ 0 to an extensive complexity of the spin glass state. 
Wednesday, March 16, 2022 4:00PM  4:12PM 
Q63.00006: Superconductormetal transition in a Hubbard model with random interactions. Chenyuan Li, Darshan G Joshi, Grigory Tarnopolsky, Subir Sachdev We present a BCS theory of superconductivity for a Hubbard model with attractive onsite interaction U along with random and alltoall hopping, exchange as well as Cooperpair hopping. The analysis is carried out in the largeM limit, where M corresponds to generalizing the SU(2) spin symmetry to USp(M). Within the meanfield treatment we find that the effect of Cooperpair hopping is on the same footing as that of the exchange interaction. In our model, we prove the existence of a BCStype log divergence in the gap equation, which implies superconductivity at zero temperature in the presence of an infinitesimal attractive Hubbard interaction. The superconductivity in our model arises out of a Fermiliquid metal for small exchange interaction, while it arises from a SYKlike nonFermiliquid metal at very large interactions. We calculate the value of the critical temperature (T_{c}) and the superconducting gap as a function of the exchange interaction and find that T_{c} decreases for intermediate values of exchange interactions. Our model may be relevant to twodimensional disordered superconductors. 
Wednesday, March 16, 2022 4:12PM  4:24PM 
Q63.00007: Multiflavor SYK model on the lattice Andrew K Hardy, Arijit Haldar, Arun Paramekanti The SachdevYeKitaev (SYK) model is a canonical solvable model of a nonFermi liquid. We study the physics of a multiflavor SYK model on the lattice and discuss its spectral properties in the presence and absence of particlehole symmetry breaking. These flavours, which can be thought of as emulating fermion spins or orbitals, along with the underlying lattice, connect the phases observed in our model to intriguing experimental observations. Using numerical and analytic calculations, we illustrate the existence of quantum phase transitions and multicritical phenomena in our model, and discuss transport properties in the largeN limit. 
Wednesday, March 16, 2022 4:24PM  4:36PM 
Q63.00008: Superconductivity and localization near a twodimensional ferromagnetic quantum critical point Pavel Nosov, Igor Burmistrov, Srinivas Raghu We study the influence of disorder on the superconducting transition in a twodimensional Fermi liquid coupled to the soft Isingferromagnetic orderparameter fluctuations associated with proximity to a quantum critical point. We determine the superconducting transition temperature, the temperature dependence of the resistivity, and the phase diagram. The analysis is based on the renormalization group for a modified nonlinear sigma model developed by us in [1]. We demonstrate that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions leading to a possible strong enhancement of superconductivity, eventually followed by the superconductorinsulator transition. 
Wednesday, March 16, 2022 4:36PM  4:48PM 
Q63.00009: Deconfined criticality and gapless Z2 spin liquids in the square lattice antiferromagnet Henry J Shackleton, Subir Sachdev, Alex R Thomson The theory for the vanishing of Néel order in the spin S=1/2 square lattice antiferromagnet has been the focus of attention for many decades. Recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the J1−J2 model) suggest the presence of a gapless Z2 spin liquid for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z2 spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the 'πflux' phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithmsquared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z2 spin liquid; on the other side of the critical point, the U(1) spin liquid (the 'staggered flux' phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent z≠1, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J2/J1: Néel, gapless Z2 spin liquid, and valence bond solid. 
Wednesday, March 16, 2022 4:48PM  5:00PM 
Q63.00010: Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: Transport and chaos Evyatar Tulipman, Erez Berg We study properties of thermal transport and quantum manybody chaos in a lattice model with $N\to\infty$ oscillators per site, coupled by strong anharmonic terms. We first consider a model with only optical phonons. We find that the thermal diffusivity $D_{\rm th}$ and chaos diffusivity $D_L$ (defined as $D_L = v_B^2/ \lambda_L$, where $v_B$ and $\lambda_L$ are the butterfly velocity and the scrambling rate, respectively) satisfy $D_{\rm th} \approx \gamma D_L$ with $\gamma\gtrsim 1$. At intermediate temperatures, the model exhibits a ``quantum phonon fluid'' regime, where both diffusivities satisfy $D^{1} \propto T$, and the thermal relaxation time and inverse scrambling rate are of the order the of Planckian timescale $\hbar/k_B T$. We then introduce acoustic phonons to the model and study their effect on transport and chaos. The longwavelength acoustic modes remain longlived even when the system is strongly coupled, due to Goldstone's theorem. As a result, for $d=1,2$, we find that $D_{\rm th}/D_L\to \infty$, while for $d=3$, $D_{\rm th}$ and $D_{L}$ remain comparable. 
Wednesday, March 16, 2022 5:00PM  5:12PM 
Q63.00011: Quantum thermal transport in the charged SachdevYeKitaev model: Thermoelectric Coulomb blockade Andrei Pavlov, Mikhail Kiselev We present a microscopic theory for quantum thermoelectric and heat transport in the Schwarzian regime of the SachdevYeKitaev (SYK) model. As a charged fermion realization of the SYK model in nanostructures, we assume a setup based on a quantum dot connected to the charge reservoirs through weak tunnel barriers. We analyze particlehole symmetry breaking effects crucial for both Seebeck and Peltier coefficients. We show that the quantum charge and heat transport at low temperatures are defined by the interplay between elastic and inelastic processes such that the inelastic processes provide a leading contribution to the transport coefficients at the temperatures that are smaller compared to the charging energy. We demonstrate that both electric and thermal conductance obey a power law in temperature behavior, while thermoelectric, Seebeck, and Peltier coefficients are exponentially suppressed. This represents selective suppression of only nondiagonal transport coefficients. We discuss the validity of the Kelvin formula in the presence of a strong Coulomb blockade. 
Wednesday, March 16, 2022 5:12PM  5:24PM 
Q63.00012: SachdevYeKitaev circuits for braiding and charging Majorana zero modes Jan Behrends, Benjamin Béri The SachdevYeKitaev (SYK) model is an alltoall interacting Majorana fermion model for manybody quantum chaos and the holographic correspondence. Here we construct fermionic alltoall Floquet quantum circuits of random fourbody gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely chargingmediated interactions and braiding Majorana zero modes. This offers an analogdigital route to SYK quantum simulations that reconciles alltoall interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including outoftimeordered, correlation functions can be measured in such analogdigital implementations by employing foreseen capabilities in Majorana devices. 
Wednesday, March 16, 2022 5:24PM  5:36PM 
Q63.00013: Plaquettedimer liquid beyond renormalization Yizhi You, Roderich Moessner We consider closepacked tiling models of geometric objects  a mixture of hardcore dimers and plaquettes  as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a zlink or a plaquettein the xy plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fractontype `higherrank electrostatics', which can exhibit a plaquettedimer liquid and an ordered phase. We analyse this theory in detail, using height representations and Tduality to demonstrate that the concomitant phase transition occurs due to the proliferation of dipoles formed by defect pairs. The resultant critical theory can be considered as a fracton version of the KosterlitzThouless transition. A significant new element is its UVIR mixing, where the low energy behavior of the liquid phase and the transition out of it is dominated by local (shortwavelength) fluctuations, rendering the critical phenomenon beyond the renormalization group paradigm. 
Wednesday, March 16, 2022 5:36PM  5:48PM 
Q63.00014: Quantum critical behavior of ultracold bosons in the twodimensional BoseHubbard lattice Sayak Ray, Ulli Pohl, Johann Kroha We investigate the temperaturedependent behavior emerging in the vicinity of the superfluid (SF) to Mott insulator (MI) transition of interacting bosons in a twodimensional optical lattice, described by the BoseHubbard model. The equilibrium phase diagram at finite temperatures is computed by means of the cluster meanfield theory (CMF) where the effect of nonlocal correlations is analyzed systematically by finitesize scaling of the clusters. The phase diagram exhibits a transition and a crossover of the SF and MI phases, respectively, to a normal fluid (NF) state at finite temperature. In order to characterize these phases, and the NF transition and crossover scales, we calculate, in addition to the condensate amplitude, the superfluid fraction, sound velocity and compressibility. The phase boundaries obtained by CMF with finitesize scaling agree quantitatively with quantum Monte Carlo (QMC) results, as well with experiments. The von Neumann entanglement entropy within a cluster exhibits critical enhancement near the SFMI quantum critical point (QCP) and at the SFNF boundary. We also discuss the behavior of the transition lines near this QCP at the particlehole symmetric point located at the tip of a Mott lobe as well as away from particlehole symmetry. 
Wednesday, March 16, 2022 5:48PM  6:00PM 
Q63.00015: Effect of acoustic phonons on quantum criticality Abhisek Samanta, Efrat Shimshoni, Daniel Podolsky We study the fate of quantum criticality in a spin system coupled to gapless phonons. In one dimension, a recent study based on renormalization group (RG) analysis and density matrix renormalization group (DMRG) calculations reveals the possibility of the transition to remain secondorder or driven to firstorder, depending on the ratio of velocities of the spins and the phonons. Our goal is to understand how the coupling affects the transition in higher dimensions. We did a perturbative RG analysis of the Φ^{4} theory coupled to acoustic phonons, using an ε expansion near (3+1) dimensions. Our analysis is supplemented by a Quantum Monte Carlo simulation of the coupled system in two and three dimensions. 
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