arXiv subjects

Zhaoyu Han

Publications and source records attributed to Zhaoyu Han.

32 records · Page 2Linked to original sources

arXiv2024

Quantum spin liquid from electron-phonon coupling

A quantum spin liquid (QSL) is an exotic insulating phase with emergent gauge fields and fractionalized excitations. However, the unambiguous demonstration of the existence of a QSL in a "non-engineered" microscopic model (or in any material) remains challenging. Here, using numerically-exact sign-problem-free quantum Monte Carlo simulations, we show that a QSL arises in a non-engineered electron-phonon model. Specifically, we investigate the ground-state phase diagram of the bond Su-Schrieffer-Heeger (SSH) model on a 2D triangular lattice at half filling (one electron per site) which we show includes a QSL phase which is fully gapped, exhibits no symmetry-breaking order, and supports deconfined fractionalized holon excitations. This suggests new routes for finding QSLs in realistic materials and high-$T_c$ superconductivity by lightly doping them.

cond-mat.str-el↗

arXiv2024

Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator

We investigate the large Kondo coupling limit of the Kondo-Heisenberg model on one- and two-dimensional lattices. Focusing on the possible superconducting states when slightly doping the Kondo insulator state, we identify different pairing modes to be most stable in different parameter regimes. Possibilities include uniform $s$-wave, pair-density-wave with momentum $π$ (in both one and two dimensions) and uniform $s\pm \mathrm{i}d_{x^2-y^2}$-wave (in two dimensions). We attribute these exotic pairing states to the presence of various pair-hopping terms with a ``wrong'' sign in the effective model, a mechanism that is likely universal for inducing pairing states with spatially modulated pair wavefunctions.

cond-mat.str-el↗

arXiv2024

Anomalous Landau level gaps near magnetic transitions in monolayer WSe$_2$

First-order phase transitions produce abrupt changes to the character of both ground and excited electronic states. Here we conduct electronic compressibility measurements to map the spin phase diagram and Landau level (LL) energies of monolayer WSe$_2$ in a magnetic field. We resolve a sequence of first-order phase transitions between completely spin-polarized LLs and states with LLs of both spins. Unexpectedly, the LL gaps are roughly constant over a wide range of magnetic fields below the transitions, which we show reflects a preference for opposite spin excitations of the spin-polarized ground state. These transitions also extend into compressible regimes, with a sawtooth boundary between full and partial spin polarization. We link these observations to the important influence of LL filling on the exchange energy beyond a smooth density-dependent contribution. Our results show that WSe$_2$ realizes a unique hierarchy of energy scales where such effects induce re-entrant magnetic phase transitions tuned by density and magnetic field.

cond-mat.mes-hall↗

arXiv2023

Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect

We propose a two-fluid description of fractional quantum Hall systems, in which one component is a condensate of composite bosons and the other a Fermi liquid formed by composite fermions (or simply electrons). We employ the theory to model the interface between a fractional quantum Hall liquid and a (composite) Fermi liquid metal, where we find a penetration of quantum Hall condensate into the metallic region reminiscent of the proximity effect in superconductor-metal interfaces. We also find a novel and physically reasonable set of gapped quasielectron and neutral modes in fractional quantum Hall liquids.

cond-mat.str-el↗

arXiv2023

Semi-classical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model

We analyze the transition temperature $T_c$ of bipolaronic superconductivity in a bond Su-Schrieffer-Heeger (bond-SSH) model -- also known as a bond Peierls model -- where the electron hoppings are modulated by bond phonons. Using a semiclassical instanton approximation justifiable in the adiabatic limit of slow phonons, we find that the bipolaron mass is only weakly enhanced, in contrast to the typical large mass enhancement found in standard (Holstein) electron-phonon models. Specifically, in the strong coupling limit, the bipolarons can freely slide within a degenerate manifold rather than become self-trapped. A gas of these bipolarons can undergo a superfluid transition at a critical temperature for which we obtain an upper bound. We find that this bound is exponentially larger than that in the Holstein model. Our study provides an analytical understanding of the mechanism behind the high-$T_c$ bipolaronic superconductivity numerically observed in [Phys. Rev. X 13, 011010 (2023)].

cond-mat.supr-con↗

arXiv2023

Resonating Valence Bond States in an Electron-Phonon System

We study a simple electron-phonon model on square and triangular versions of the Lieb-lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density $n = 1$ (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with $\mathbb{Z}_2$ topological order (on the triangular lattice) and a multi-critical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (e.g. valence-bond crystals), a conventional s-wave superconducting phase, and with the addition of a small Hubbard $U$ to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudo-spin $SU(2)$ symmetry that implies an exact constraint on the superconducting order parameters.

cond-mat.str-el↗

arXiv2023

Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians

The Kapustin-Fidkowski no-go theorem forbids $U(1)$ symmetric topological orders with non-trivial Hall conductivity in (2+1)d from admitting commuting projector Hamiltonians, where the latter is the paradigmatic method to construct exactly solvable lattice models for topological orders. Even if a topological order would intrinsically have admitted commuting projector Hamiltonians, the theorem forbids so once its interplay with $U(1)$ global symmetry which generates Hall conductivity is taken into consideration. Nonetheless, in this work, we show that for all (2+1)d $U(1)$ symmetric abelian topological orders of such kind, we can construct a lattice Hamiltonian that is controllably solvable at low energies, even though not "exactly" solvable; hence, this no-go theorem does not lead to significant difficulty in the lattice study of these topological orders. Moreover, for the fermionic topological orders in our construction, we introduce the lattice notion of spin-c structure -- a concept important in the continuum that has previously not been adequately introduced in the lattice context.

cond-mat.str-el↗

arXiv2022

The one-dimensional Holstein model revisited

We analyze the global ground-state (quantum) phase diagram of the one-dimensional Holstein model at half-filling as a function of the strength of the electron-phonon coupling (represented by the strength of the phonon-induced attraction, $U$) and the phonon frequency, $ω_0$. In addition to reanalyzing the various asymptotic regimes, we have carried out density-matrix renormalization group simulations to correct previous inferences concerning the anti-adiabatic (large $ω_0$) and strong coupling (large $U$) regimes. There are two distinct phases - a fully gapped commensurate charge-density-wave and a spin-gapped Luther-Emery phase with a gapless charge mode - separated by a phase boundary, with a shape that reflects different microscopic physics in the weak and strong coupling limits.

cond-mat.str-el↗

arXiv2022

Solvable Lattice Hamiltonians with Fractional Hall Conductivity

We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.

cond-mat.str-el↗

arXiv2022

Pair density wave and reentrant superconducting tendencies originating from valley polarization

We investigate superconducting pairing tendencies of a two-dimensional electron fluid with both valley and spin degrees of freedom, both without and in the presence of an in-plane magnetic field. We present suggestive theoretical arguments that spontaneous valley polarization can lead to exotic singlet superconducting tendencies, including pair-density-wave order at zero field and re-entrant superconductivity at high field. We also find a reduced magnetic response in the polarized valley, which allows a finite violation of the Pauli limit. These results are obtained by a mean-field approach to a generalized $t$-$J$ model on a triangular lattice and in the dilute limit. Phenomenological similarities to results of recent magic-angle twisted trilayer graphene experiments are noted.

cond-mat.supr-con↗

arXiv2022

Pair-Density-Wave in the Strong Coupling Limit of the Holstein-Hubbard model

A pair-density-wave (PDW) is a novel superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a density-matrix renormalization group (DMRG) study of an effective $t$-$J$-$V$ model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four- and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as the spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the $K$ and $K^\prime$ points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge $c\approx 1$ are consistent with an unusual realization of a Luther-Emery liquid.

cond-mat.str-el↗

arXiv2021

Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene

In magic angle twisted bilayer graphene (MATBG), the moiré superlattice potential gives rise to narrow electronic bands1 which support a multitude of many-body quantum phases. Further richness arises in the presence of a perpendicular magnetic field, where the interplay between moiré and magnetic length scales leads to fractal Hofstadter subbands. In this strongly correlated Hofstadter platform, multiple experiments have identified gapped topological and correlated states, but little is known about the phase transitions between them in the intervening compressible regimes. Here, using a scanning single-electron transistor microscope to measure local electronic compressibility, we simultaneously unveil novel sequences of broken-symmetry Chern insulators (CIs) and resolve sharp phase transitions between competing states with different topological quantum numbers and spin/valley flavor occupations. Our measurements provide a complete experimental mapping of the energy spectrum and thermodynamic phase diagram of interacting Hofstadter subbands in MATBG. In addition, we observe full lifting of the degeneracy of the zeroth Landau levels (zLLs) together with level crossings, indicating moiré valley splitting. We propose a unified flavor polarization mechanism to understand the intricate interplay of topology, interactions, and symmetry breaking as a function of density and applied magnetic field in this system.

cond-mat.str-el↗

arXiv2020

Strong Coupling Limit of the Holstein-Hubbard Model

We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong-coupling expansion. We find all sorts of interesting phases including a pair-density wave (PDW), a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave (CDW), spin-density-wave (SDW) and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e. the ratio of characteristic phonon frequency to the strength of interactions.

cond-mat.str-el↗

arXiv2019

Charge Density Waves in a Quantum Plasma

We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios, against charge and spin density waves (CDWs and SDWs). Using density functional theory, we treat each component with the local spin density approximation and a rescaled exchange-correlation functional. Interactions between different components are treated with a mean-field approximation. In both two- and three-dimensions, we find leading unstable CDW modes in the second-order expansion of the energy functional, which would induce the transition to quantum liquid crystals. The transition point and the length of the wave-vector are computed numerically. Discontinuous ranges of the wave-vector are found for different mass ratios between the two components, indicating exotic quantum phase transitions. Phase diagrams are obtained and a scaling relation is proposed to generalize the results to two-component fermionic plasmas with any mass scale. We discuss the implications of our results and directions for further improvement in treating quantum plasmas.

cond-mat.str-el↗