arXiv subjects

Guo-Yi Zhu

Publications and source records attributed to Guo-Yi Zhu.

33 records · Page 2Linked to original sources

arXiv2023

Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements

In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled states lead to phases of matter which are stable to gate imperfections, which can convert projective into weak measurements. Here we show that in certain cases, long-range entanglement persists in the presence of weak measurements, and gives rise to novel forms of quantum criticality. We demonstrate this explicitly for preparing the two-dimensional Greenberger-Horne-Zeilinger cat state and the three-dimensional toric code as minimal instances. In contrast to the monitored random unitary circuits, In contrast to random monitored circuits, our circuit of gates and measurements is deterministic; the only randomness is in the measurement outcomes. We show how the randomness in these weak measurements allows us to track the solvable Nishimori line of the random-bond Ising model, rigorously establishing the stability of the glassy long-range entangled states in two and three spatial dimensions. Away from this exactly solvable construction, we use hybrid tensor network and Monte Carlo simulations to obtain a nonzero Edwards-Anderson order parameter as an indicator of long-range entanglement in the two-dimensional scenario. We argue that our protocol admits a natural implementation in existing quantum computing architectures, requiring only a depth-3 circuit on IBM's heavy-hexagon transmon chips.

quant-ph↗

arXiv2023

Qubit fractionalization and emergent Majorana liquid in the honeycomb Floquet code induced by coherent errors and weak measurements

From the perspective of quantum many-body physics, the Floquet code of Hastings and Haah can be thought of as a measurement-only version of the Kitaev honeycomb model where a periodic sequence of two-qubit XX, YY, and ZZ measurements dynamically stabilizes a toric code state with two logical qubits. However, the most striking feature of the Kitaev model is its intrinsic fractionalization of quantum spins into an emergent gauge field and itinerant Majorana fermions that form a Dirac liquid, which is absent in the Floquet code. Here we demonstrate that by varying the measurement strength of the honeycomb Floquet code one can observe features akin to the fractionalization physics of the Kitaev model at finite temperature. Introducing coherent errors to weaken the measurements we observe three consecutive stages that reveal qubit fractionalization (for weak measurements), the formation of a Majorana liquid (for intermediate measurement strength), and Majorana pairing together with gauge ordering (for strong measurements). Our analysis is based on a mapping of the imperfect Floquet code to random Gaussian fermionic circuits (networks) that can be Monte Carlo sampled, exposing two crossover peaks. With an eye on circuit implementations, our analysis demonstrates that the Floquet code, in contrast to the toric code, does not immediately break down to a trivial state under weak measurements, but instead gives way to a long-range entangled Majorana liquid state.

quant-ph↗

arXiv2023

Topological fracton quantum phase transitions by tuning exact tensor network states

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a $\mathbb{Z}_N$ generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wavefunction deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the $\mathbb{Z}_N$ model we find a family of (weakly) first-order fracton confinement transitions that in the limit of $N\to\infty$ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the $N\to\infty$ limit, appears to coexist with a gapless deconfined fracton state.

cond-mat.str-el↗

arXiv2023

Structured volume-law entanglement in an interacting, monitored Majorana spin liquid

Monitored quantum circuits allow for unprecedented dynamical control of many-body entanglement. Here we show that random, measurement-only circuits, implementing the competition of bond and plaquette couplings of the Kitaev honeycomb model, give rise to a structured volume-law entangled phase with subleading $L \ln L$ liquid scaling behavior. This interacting Majorana liquid takes up a highly-symmetric, spherical parameter space within the entanglement phase diagram obtained when varying the relative coupling probabilities. The sphere itself is a critical boundary with quantum Lifshitz scaling separating the volume-law phase from proximate area-law phases, a color code or a toric code. An exception is a set of tricritical, self-dual points exhibiting effective (1+1)d conformal scaling at which the volume-law phase and both area-law phases meet. From a quantum information perspective, our results define error thresholds for the color code in the presence of projective error and stochastic syndrome measurements. We show that an alternative realization of our model circuit can be implemented using unitary gates plus ancillary single-qubit measurements only.

quant-ph↗

arXiv2021

Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium

Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories. In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics. We study a Kitaev honeycomb model in a skew magnetic field subject to a quantum quench from a fully polarized initial product state and observe nonergodic dynamics as a consequence of disorder-free localization. We find that the system exhibits a subballistic power-law entanglement growth and quantum correlation spreading, which is otherwise typically associated with thermalizing systems. In the asymptotic steady state the Kitaev model develops volume-law entanglement and power-law decaying dimer quantum correlations even at a finite energy density. Our work sheds light onto the potential for disorder-free localized lattice gauge theories to realize quantum states in two dimensions with properties beyond what is possible in an equilibrium context.

cond-mat.str-el↗

arXiv2019

Gapless Coulomb state emerging from a self-dual topological tensor-network state

In the tensor network representation, a deformed $Z_{2}$ topological ground state wave function is proposed and its norm can be exactly mapped to the two-dimensional solvable Ashkin-Teller (AT) model. Then the topological (toric code) phase with anyonic excitations corresponds to the partial order phase of the AT model, and possible topological phase transitions are precisely determined. With the electric-magnetic self-duality, a novel gapless Coulomb state with quasi-long-range order is obtained via a quantum Kosterlitz-Thouless phase transition. The corresponding ground state is a condensate of pairs of logarithmically confined electric charges and magnetic fluxes, and the scaling behavior of various anyon correlations can be exactly derived, revealing the effective interaction between anyons and their condensation. Deformations away from the self-duality drive the Coulomb state into either the gapped Higgs phase or confining phase.

cond-mat.str-el↗

arXiv2018

Spin-valley antiferromagnetism and topological superconductivity in the trilayer graphene Moire super-lattice

Exotic correlated insulating phases emerge in the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at both quarter and half-filling. A single-band minimal model with valley contrasting staggered-flux is proposed to capture the relevant band structure, where the conspiracy of perfect Fermi-surface nesting and van Hove singularity strongly enhance the valley fluctuation, leading to inter-valley spiral (IVS) order at half filling. In this paper, we consider a strong coupling U(1)$_{v}\times $SU(2)$_{s}$ symmetric spin-valley model to obtain the correlated insulating state and the pairing instability near quarter filling. A significant ingredient in the strong coupling model is the Dzyaloshinsky-Moriya like interaction inherited from the flux, which breaks not only the valley SU(2)$_{v}$ symmetry but also the sub-valley spatial reflection symmetry. We discuss all the possible long-range orders stabilized by the effective spin-valley-exchange interactions, and it turns out that the flux remarkably enhance the ferro-spin inter-valley 120$^{\circ}$ order, which shares the same valley feature as the IVS order. Upon doping, the leading pairing instability lies in the inter-valley channel with a trigonally warped $p\pm ip$-wave form factor in the presence of the sub-valley reflection symmetry breaking. Depending on the sign of Hund's coupling, the total pairing state could be either spin singlet or triplet. While the spin singlet chiral topological pairing state $(p\pm ip)_{\uparrow\downarrow }-(p\pm ip)_{\downarrow \uparrow }$ is necessarily chiral, the spin triplet topological pairing state could be chiral $(p\pm ip)_{\uparrow\uparrow }+(p\pm ip)_{\downarrow \downarrow }$, or helical $(p\pm ip)_{\uparrow \uparrow }+(p\mp ip)_{\downarrow \downarrow }$.

cond-mat.str-el↗

arXiv2018

Decoding quantum criticalities from fermionic/parafermionic topological states

Under an appropriate symmetric bulk bipartition in a one-dimensional symmetry protected topological phase with the Affleck-Kennedy-Lieb-Tasaki matrix product state wave function for the odd integer spin chains, a bulk critical entanglement spectrum can be obtained, describing the excitation spectrum of the critical point separating the topological phase from the trivial phase with the same symmetry. Such a critical point is beyond the standard Landau-Ginzburg-Wilson paradigm for symmetry breaking phase transitions. Recently, the framework of matrix product states for topological phases with Majorana fermions/parafermions has been established. Here we first generalize these fixed-point matrix product states with the zero correlation length to the more generic ground-state wave functions with a finite correlation length for the general one-dimensional interacting Majorana fermion/parafermion systems. Then we employ the previous method to decode quantum criticality from the interacting Majorana fermion/parafermion matrix product states. The obtained quantum critical spectra are described by the conformal field theories with central charge $c\leq 1$, characterizing the quantum critical theories separating the fermionic/parafermionic topological phases from the trivial phases with the same symmetry.

cond-mat.str-el↗

arXiv2018

Inter-valley spiral order in the Mott insulating state of a heterostructure of trilayer graphene-boron nitride

Recent experiment has shown that the ABC-stacked trilayer graphene-boron nitride Moire super-lattice at half-filling is a Mott insulator. Based on symmetry analysis and effective band structure calculation, we propose a valley-contrasting chiral tight-binding model with local Coulomb interaction to describe this Moire super-lattice system. By matching the positions of van Hove points in the low-energy effective bands, the valley-contrasting staggered flux per triangle is determined around $π/2$. When the valence band is half-filled, the Fermi surfaces are found to be perfectly nested between the two valleys. Such an effect can induce an inter-valley spiral order with a gap in the charge excitations, indicating that the Mott insulating behavior observed in the trilayer graphene-boron nitride Moire super-lattice results predominantly from the inter-valley scattering.

cond-mat.str-el↗

arXiv2017

Plaquette-centered rotation symmetry and octet-nodal superconductivity in $\text{KFe}_{2}\text{As}_{2}$

A plaquette-centered rotation symmetry $C_{4}^{p}$ is identified to play a significant role in determining and stabilizing the Fermi-surface structure of Fe-based superconductors. Together with the $S_{4}$ symmetry previously found, we are able to sort out the tangling orbitals and solve the puzzle of pairing symmetry of superconductivity in $\text{KFe}_{2}\text{As}_{2}$ in a simple but comprehensive way. By modeling the material with a strong coupling $t-J_{1}-J_{2}$ model, we find phase transitions of pairing symmetry driven by the competition between the local spin antiferromagnetic couplings from nodal $d_{x^2-y^2}\times s_{x^2+y^2}$-wave to nodeless $% s_{x^2 y^2} $-wave through the intermediate $s+id\times s$ mixed pairing phase, which is consistent with the observation of pressure experiments. The emergent $d$-wave form factor inevitably arises from the projection of inter-orbital Cooper pairing onto the Fermi surface and is inherited from the electronic structure in the representation of $C_{4}^{p}$ symmetry. Moreover, the $S_{4}$ symmetry dictates 2 copies of $d$-wave pairing condensates, counting 8 nodes in total. We further show that weakly breaking $C_{4}^{p}$ naturally leads to the octet nodal gap as precisely observed in laser angle resolved photoemission spectroscopy. The octet nodes reflect the collaboration of the $C_{4}^{p}$ and $S_{4}$ symmetries, which sheds new light on the enigma of the pairing symmetry in $\text{KFe}_{2}\text{As}_{2}$.

cond-mat.supr-con↗

arXiv2017

Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.

cond-mat.supr-con↗

arXiv2017

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO$_{2}$ grown on the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional $t$-$J$ model in proximity to an antiferromagnetic (AF) insulator. We found that (i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity induced AF field. (ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. (iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with ($s+$i$d$) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a $Z_{2}$ topological superconductor protected by valley symmetry, exhibiting robust gapless non-chiral edge modes. These findings strongly suggest that the high-$T_{c}$ superconductors in proximity to antiferromagnets can realize fully gapped symmetry protected topological SC.

cond-mat.supr-con↗

arXiv2016

Proximity induced superconductivity in monolayer CuO$_{2}$ on the cuprate substrates

To understand the recently observed high temperature superconductivity in the monolayer CuO$_2$ grown on the Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ substrates, we propose a two band model of the hybridized oxygen $p_x$ and $p_y$ orbitals with the proximity effect of the substrate. We demonstrate that both the nodal and nodeless d-wave superconducting states can be induced by the proximity effect, depending on the strengths of the pairing parameters.

cond-mat.supr-con↗

arXiv2016

SU(3) quantum critical model emerging from a spin-1 topological phase

Different from the spin-1 Haldane gapped phase, we propose a novel SO(3) spin-1 matrix product state (MPS), whose parent Hamiltonian includes three-site spin interactions. From the entanglement spectrum of a single block with $l$ sites, an enlarged SU(3) symmetry is identified in the edge states, which are conjugate to each other for the $l=even$ block but identical for the $l=odd$ block. By blocking this novel state, the blocked MPS explicitly displays the SU(3) symmetry with two distinct structures. Under a symmetric bulk bipartition with a sufficient large block length $% l=even$, the entanglement Hamiltonian (EH) of the reduced system characterizes a spontaneous dimerized phase with two-fold degeneracy. However, for the block length $l=odd$, the corresponding EH represents an SU(3) quantum critical point with delocalized edge quasiparticles, and the critical field theory is described by the SU(3) level-1 Wess-Zumino-Witten conformal field theory.

cond-mat.str-el↗

arXiv2015

Conductance and shot noise in the helimagnet tunnel junction

As a result of sinusoidal spatial modulation, helimagnet induces spin-dependent diffracted transmission. In this work, we propose a general scattering matrix treatment to the transport properties in helimagnets with arbitrary helical structures. Multiferroic properties can be considered by taking electric polarization and magnetic helix together into account. A monolayer magnetic helix can be treated as a $δ$-barrier by diffraction theory. The conductance and shot noise properties of the normal metal/helimagnet/normal metal toy model are investigated. It is found that the shot noise is suppressed and demonstrates rise-and-fall variations as a result of interference between different diffracted channels. Sharp change of the shot noise occurs when one and both diffracted beams disappear into evanescent modes at the helimagnet spiral wave vector equal to one and two times the electron Fermi wave vector $q=k_F$ and $2 k_F$. We also considered the conductance and shot noise properties in a real multiferroic helimagnet $\rm{TbMnO_3}$ with ferroelectric and helimagnetism coexistent. It is found that clockwise and counterclockwise spin helix is distinctly separated in the conductance and shot noise spectrum. Their variation pattern is a combined result of helimagnetism and electric polarization.

cond-mat.mes-hall↗