arXiv subjects

Yi-Zhuang You

Publications and source records attributed to Yi-Zhuang You.

At least 91 records · Page 5Linked to original sources

arXiv2019

Gauge Enhanced Quantum Criticality and Time Reversal Domain Wall: SU(2) Yang-Mills Dynamics with Topological Terms

We explore the low energy dynamics of the four siblings of Lorentz symmetry enriched SU(2) Yang-Mills theory with a theta term at $θ=π$ in $(3+1)$d. Due to a mixed anomaly between time reversal symmetry and the center symmetry, the low energy dynamics must be nontrivial. We focus on two possible scenarios: 1) time reversal symmetry is spontaneously broken by the two confining vacua, and 2) the low energy theory is described by a U(1) Maxwell gauge theory (e.g. U(1) spin liquid in condensed matter) which is deconfined and gapless while preserving time reversal symmetry. In the first scenario, we first identify the global symmetry on the time reversal domain wall, where time reversal symmetry in the bulk induces a $\mathbb{Z}_2$ unitary symmetry on the domain wall. We discuss how the Lorentz symmetry and the unitary $\mathbb{Z}_2$ symmetry enrich the domain wall theory. In the second scenario, we relate the symmetry enrichments of the SU(2) Yang-Mills to that of the U(1) Maxwell gauge theory. This further opens up the possibility that SU(2) QCD with large and odd flavors of fermions could be a direct second order phase transition between two phases of U(1) gauge theories as well as between a U(1) gauge theory and a trivial vacuum (e.g. a trivial paramagnet), where the gauge group is enhanced to be non-Abelian at and only at the transition. We characterize these transitions, and name them as Gauge Enhanced Quantum Critical Points.

cond-mat.str-el↗

arXiv2019

Entanglement Transitions from Holographic Random Tensor Networks

We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the "holographic" boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.

cond-mat.stat-mech↗

arXiv2019

Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu$_2$(BO$_3$)$_2$

We study a possible deconfined quantum phase transition in a realistic model of a two-dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. Using the infinite density matrix renormalization group (iDMRG) method, we verify the existence of an intermediate plaquette valence bond solid (pVBS) order, with two fold degeneracy, between the dimer and Néel ordered phases. We argue that the quantum phase transition between the Néel and pVBS orders may be described by a deconfined quantum critical point (DQCP) with an emergent O(4) symmetry. By analyzing the correlation length spectrum obtained from iDMRG, we provide evidence for the DQCP and emergent O(4) symmetry in the lattice model. Such a phase transition has been reported in the recent pressure tuned experiments in the Shastry-Sutherland lattice material $\mathrm{SrCu_2 (BO_3)_2}$. The non-symmorphic lattice structure of the Shastry-Sutherland compound leads to extinction points in the scattering, where we predict sharp signatures of a DQCP in both the phonon and magnon spectra associated with the spinon continuum. The effect of weak interlayer couplings present in the three dimensional material is also discussed. Our results should help guide the experimental study of DQCP in quantum magnets.

cond-mat.str-el↗

arXiv2019

Machine Learning Holographic Mapping by Neural Network Renormalization Group

The exact holographic mapping (EHM) provides an explicit duality map between a conformal field theory (CFT) configuration and a massive field propagating on an emergent classical geometry. However, designing the optimal holographic mapping is challenging. Here we introduce the neural network renormalization group as a universal approach to design generic EHM for interacting field theories. Given a field theory action, we train a flow-based hierarchical deep generative neural network to reproduce the boundary field ensemble from uncorrelated bulk field fluctuations. In this way, the neural network develops the optimal renormalization group transformations. Using the machine-designed EHM to map the CFT back to a bulk effective action, we determine the bulk geodesic distance from the residual mutual information. We apply this approach to the complex $ϕ^4$ theory in two-dimensional Euclidian spacetime in its critical phase, and show that the emergent bulk geometry matches the three-dimensional hyperbolic geometry.

cond-mat.dis-nn↗

arXiv2019

Measurement-induced criticality in random quantum circuits

We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the $n$th Rényi entropies for $n \geq 1$ in this limit using relatively recent results for conformal field theory describing the critical theory of 2D percolation, and we discuss how to access the generic transition at finite on-site Hilbert space dimension from this limit, which is in a universality class different from 2D percolation. We also comment on the relation to the entanglement transition in Random Tensor Networks, studied previously in Ref. 1.

cond-mat.stat-mech↗

arXiv2019

Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor

Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor ($N_f$) and the strength of gauge fluctuations is mapped out~\cite{Xiao2018Monte}. Here we focus on the large fermion flavor case ($N_f=8$) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED$_3$-Gross-Neveu chiral O(2) universality whose properties still largely unknown.

cond-mat.str-el↗

arXiv2019

Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model

The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality.

quant-ph↗

arXiv2019

Emergent Quantum Mechanics in an Introspective Machine Learning Architecture

Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schrödinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schrödinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.

cond-mat.dis-nn↗

arXiv2019

Emmy Noether looks at the deconfined quantum critical point

Noether's theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether's theorem at the deconfined quantum critical point (DQCP), which is the quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to emerged conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent symmetry by probing the spin excitations, which could potentially guide the ongoing experimental search for DQCP in quantum magnets.

cond-mat.str-el↗

arXiv2019

Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene

We develop a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($d+i d$ mixed with $p-i p$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three M points in the Brillouin Zone, and a $2\times2$ pattern in real space. In simple treatments though, this leads to a full gap at fillings $\pm (1/2+1/8)$, slightly away from half-filling. An SO(4) symmetry breaking "anti-Hunds" coupling favors the spin-singlet order both for the IVCW and the superconductor, consistent with observations. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.

cond-mat.str-el↗

arXiv2019

Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point

The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems. While great efforts have been spent on the DQCP for 2D systems, both theoretically and numerically, ambiguities among the nature of the transition are still not completely clarified. Here we shift the focus to a recently proposed 1D incarnation of DQCP in a spin-1/2 chain. By solving it with the variational matrix product state in the thermodynamic limit, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. The scaling dimensions of various operators are calculated and compared with those from field theoretical description. At the critical point, two emergent O(2) symmetries are revealed, and the associated conserved current operators with exact integer scaling dimensions are determined with scrutiny. Our findings provide the low-dimensional analog of DQCP where unbiased numerical results are in perfect agreement with the controlled field theoretical predictions and have extended the realm of the unconventional phase transition as well as its identification with the advanced numerical methodology.

cond-mat.str-el↗

arXiv2019

A topological phase transition on the edge of the 2d $\mathbb{Z}_2$ topological order

The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions on the edges of 2d topological orders (without altering the bulks). In particular, it implies that the critical points are described by enriched fusion categories. In this work, we illustrate this idea in a concrete example: the 2d $\mathbb{Z}_2$ topological order. In particular, we construct an enriched fusion category, which describes a gappable non-chiral gapless edge of the 2d $\mathbb{Z}_2$ topological order; then use an explicit lattice model construction to realize the critical point and, at the same time, all the ingredients of this enriched fusion category.

cond-mat.str-el↗

arXiv2018

Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point

Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin structure factors in the $S^{x}$ and $S^{z}$ channels. In both channels, we observe broad continua that originate from the deconfined excitations. We further identify several distinct spectral features of the deconfined quantum critical point, including the lower edge of the continuum and its form factor on moving through the Brillouin Zone. We provide field-theoretical and lattice model calculations that explain the overall shapes of the computed spectra, which highlight the importance of interactions and gauge fluctuations to explaining the spectral-weight distribution. We make further comparisons with the conventional Landau O(2) transition in a different quantum magnet, at which no signatures of fractionalization are observed. The distinctive spectral signatures of the deconfined quantum critical point suggest the feasibility of its experimental detection in neutron scattering and nuclear magnetic resonance experiments.

cond-mat.str-el↗

arXiv2018

A candidate Theory for the "Strange Metal" phase at Finite Energy Window

We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high temperature superconductors. Our model is motivated by the recently developed "tetrahedron" rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it only needs one orbital per site on the square lattice; (2) it does not require any quenched random interaction; (3) it has local interactions and respects all the symmetries of the system; (4) the soluble limit of this model has a longitudinal DC resistivity that scales linearly with temperature within a finite temperature window; (5) again the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a "pseudogap" phase. The linear$-T$ longitudinal resistivity and the pairing instability originate from the generic scaling feature of the SYK model and the tetrahedron tensor model.

cond-mat.str-el↗

arXiv2018

Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D

The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a U$(1)$ gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean spacetime lattice path integral for a theory with strongly-interacting $SO(3)$ vector bosons and Majorana fermions coupled to an $SO(3)$ gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the spacetime lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an $SO(3)$ vector critical boson coupled to an $SO(3)_1$ Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with $O(3)$ gauge fields.

cond-mat.str-el↗

arXiv2018

Entanglement Features of Random Hamiltonian Dynamics

We introduce the concept of entanglement features of unitary gates, as a collection of exponentiated entanglement entropies over all bipartitions of input and output channels. We obtained the general formula for time-dependent $n$th-Renyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the 2nd-Renyi entanglement features of random Hamiltonian dynamics, which admits a holographic tensor network interpretation. As a general description of entanglement properties, we show that the entanglement features can be applied to several dynamical measures of thermalization, including the out-of-time-order correlation and the entanglement growth after a quantum quench. We also analyze the Yoshida-Kitaev probabilistic protocol for random Hamiltonian dynamics.

quant-ph↗

arXiv2018

Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions

Recently, it has been shown that two-dimensional bosonic symmetry-protected topological(SPT) phases with on-site unitary symmetry $G$ can be completely classified by the group cohomology class $H^3(G, \mathrm{U}(1))$. Later, group super-cohomology class was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the mathematical framework of $G$-extension of unitary braided tensor category(UBTC) theory. We first reproduce the partial classifications given by group super-cohomology, then we show that with an additional $H^1(G, \mathbb{Z}_2)$ structure, a complete classification of SPT phases for two-dimensional interacting fermion systems for a total symmetry group $G\times\mathbb{Z}_2^f$ can be achieved. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.

cond-mat.str-el↗

arXiv2018

Machine Learning Spatial Geometry from Entanglement Features

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS$_3$ spatial geometry) as we tune the fermion system towards the gapless critical point (CFT$_2$ point).

cond-mat.dis-nn↗