arXiv subjects

Cenke Xu

Publications and source records attributed to Cenke Xu.

At least 55 records · Page 3Linked to original sources

arXiv2022

A Multicritical Point with Infinite Fractal Symmetries

Recently a ``Pascal's triangle model" constructed with $\text{U}(1)$ rotor degrees of freedom was introduced, and it was shown that ($\textit{i}$.) this model possesses an infinite series of fractal symmetries; and ($\textit{ii}$.) it is the parent model of a series of $Z_p$ fractal models each with its own distinct fractal symmetry. In this work we discuss a multi-critical point of the Pascal's triangle model that is analogous to the Rokhsar-Kivelson (RK) point of the better known quantum dimer model. We demonstrate that the expectation value of the characteristic operator of each fractal symmetry at this multi-critical point decays as a power-law of space, and this multi-critical point is shared by the family of descendent $Z_p$ fractal models. Afterwards, we generalize our discussion to a $(3+1)d$ model termed the ``Pascal's tetrahedron model" that has both planar and fractal subsystem symmetries. We also establish a connection between the Pascal's tetrahedron model and the $\text{U}(1)$ Haah's code.

cond-mat.str-el↗

arXiv2022

Frustrated magnetic interactions in a Wigner-Mott insulator

Two-dimensional semiconductor moiré materials have emerged as a highly controllable platform to simulate and explore quantum condensed matter. Compared to real solids, electrons in semiconductor moiré materials are less strongly attracted to the moiré lattice sites, making the nonlocal contributions to the magnetic interactions as important as the Anderson super-exchange. It provides a unique platform to study the effects of competing magnetic interactions. Here, we report the observation of strongly frustrated magnetic interactions in a Wigner-Mott insulating state at 2/3 filling of the moiré lattice in angle-aligned WSe2/WS2 heterobilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at 2/3 filling. The suppression is lifted upon screening of the long-range Coulomb interactions and melting of the Wigner-Mott insulator by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model with an antiferromagnetic nearest-neighbor coupling and a ferromagnetic second-neighbor coupling. Our study establishes semiconductor moiré materials as a model system for the lattice-spin physics and frustrated magnetism.

cond-mat.mtrl-sci↗

arXiv2022

A construction of exotic metallic states

We discuss examples of two dimensional metallic states with charge fractionalization, and we will demonstrate that the mechanism of charge fractionalization leads to exotic metallic behaviors at low and intermediate temperature. The simplest example of such state is constructed by fermionic partons at finite density coupled to a $Z_N$ gauge field, whose properties can be studied through rudimentary methods. This simple state has the following exotic features: (1) at low temperature this state is a "bad metal" whose resistivity can exceed the Mott-Ioffe-Regel limit; (2) while increasing temperature $T$ the resistivity $ρ(T)$ is a nonmonotonic function, and it crosses over from a bad metal at low $T$ to a good metal at relatively high $T$; (3) the optical conductivity $σ(ω)$ has a small Drude weight at low $T$, and a larger Drude weight at intermediate $T$; (4) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law. A more complex example with fermionic partons at finite density coupled to a SU(N) gauge field will also be constructed.

cond-mat.str-el↗

arXiv2021

Self-duality protected multi-criticality in deconfined quantum phase transitions

Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a description of the deconfined quantum criticality, the $N_f=2$ QED$_3$, as an example of self-dual theories and its multi-critical behavior under perturbative deformations. The multi-criticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calculate the scaling dimensions of various operators in the 3d quantum electrodynamics with the Chern-Simons term and Gross-Neveu couplings by the large-$N$ renormalization group analysis. Specifically, we find certain non-relativistic four-fermion interactions corresponding to the dimer-dimer interactions in the lattice model will drive the deconfined quantum criticality to the first-order transition, consistent with previous numerical studies.

cond-mat.str-el↗

arXiv2021

Pascal's Triangle Fractal Symmetries

We introduce a model of interacting bosons exhibiting an infinite collection of fractal symmetries -- termed "Pascal's triangle symmetries" -- which provides a natural $U(1)$ generalization of a spin-(1/2) system with Sierpinski triangle fractal symmetries. The Pascal's triangle symmetry gives rise to exact degeneracies, as well as a manifold of low-energy states which are absent in the Sierpinski triangle model. Breaking the $U(1)$ symmetry of this model to $Z_p$, with prime integer $p$, yields a lattice model with a unique fractal symmetry which is generated by an operator supported on a fractal subsystem with Hausdorff dimension $d_H = \ln (p(p+1)/2)/\ln p$. The Hausdorff dimension of the fractal can be probed through correlation functions at finite temperature. The phase diagram of these models at zero temperature in the presence of quantum fluctuations, as well as the potential physical construction of the $U(1)$ model are discussed.

cond-mat.str-el↗

arXiv2021

Construction of Fractal Order and Phase Transition with Rydberg Atoms

We propose the construction of a many-body phase of matter with fractal structure using arrays of Rydberg atoms. The degenerate low energy excited states of this phase form a self-similar fractal structure. This phase is analogous to the so-called "type-II fracton topological states". The main challenge in realizing fracton-like models in standard condensed matter platforms is the creation of multi-spin interactions, since realistic systems are typically dominated by two-body interactions. In this work, we demonstrate that the Van der Waals interaction and experimental tunability of Rydberg-based platforms enable the simulation of exotic phases of matter with fractal structures, and the study of a quantum phase transition involving a fractal ordered phase.

cond-mat.quant-gas↗

arXiv2021

Magic continuum in twisted bilayer square lattice with staggered flux

We derive the general continuum model for a bilayer system of staggered-flux square lattices, with arbitrary elastic deformation in each layer. Applying this general continuum model to the case where the two layers are rigidly rotated relative to each other by a small angle, we obtain the band structure of the twisted bilayer staggered-flux square lattice. We show that this band structure exhibits a "magic continuum" in the sense that an exponential reduction of the Dirac velocity and bandwidths occurs in a large parameter regime. We show that the continuum model of the twisted bilayer system effectively describes a massless Dirac fermion in a spatially modulating magnetic field, whose renormalized Dirac velocity can be exactly calculated. We further give an intuitive argument for the emergence of flattened bands near half filling in the magic continuum and provide an estimation of the large number of associated nearly-zero-energy states. We also show that the entire band structure of the twisted bilayer system is free of band gaps due to symmetry constraints.

cond-mat.str-el↗

arXiv2021

Green's function Zero and Symmetric Mass Generation

It is known that, under short-range interactions many topological superconductors (TSC) and topological insulators (TI) are trivialized, which means the boundary state of the system can be trivially gapped out by interaction without leading to symmetry breaking or topological ground state degeneracy. This phenomenon is also referred to as "symmetric mass generation" (SMG), and has attracted broad attentions from both the condensed matter and high energy physics communities. However, after the trivialization caused by interaction, some trace of the nontrivial topology of the system still persists. Previous studies have indicated that interacting topological TSC and TI could be related to the "zero" of Green's function, namely the fermion Green's function $G(\mathrm{i} ω\rightarrow 0) = 0$. In this work, through the general "decorated defect" construction of symmetry protected topological (SPT) states, we demonstrate the existence of Green's function zero after SMG, by mapping the evaluation of the Green's function to the problem of a single particle path integral. This method can be extended to the cases without spatial translation symmetry, where the momentum space which hosts many quantized topological numbers is no longer meaningful. Using the same method one can demonstrate the existence of the Green's function zero at the "avoided topological transition" in the bulk of the system.

cond-mat.str-el↗

arXiv2021

Universal Features of Higher-Form Symmetries at Phase Transitions

We investigate the behavior of higher-form symmetries at various quantum phase transitions. We consider discrete 1-form symmetries, which can be either part of the generalized concept "categorical symmetry" (labelled as $\tilde{Z}_N^{(1)}$) introduced recently, or an explicit $Z_N^{(1)}$ 1-form symmetry. We demonstrate that for many quantum phase transitions involving a $Z_N^{(1)}$ or $\tilde{Z}_N^{(1)}$ symmetry, the following expectation value $ \langle \left( \log O_\mathcal{C} \right)^2 \rangle$ takes the form $\langle \left( \log O_\mathcal{C} \right)^2 \rangle \sim - \frac{A}ε P+ b \log P $, where $O_\mathcal{C}$ is an operator defined associated with loop $\mathcal{C}$ (or its interior $\mathcal{A}$), which reduces to the Wilson loop operator for cases with an explicit $Z_N^{(1)}$ 1-form symmetry. $P$ is the perimeter of $\mathcal{C}$, and the $b \log P$ term arises from the sharp corners of the loop $\mathcal{C}$, which is consistent with recent numerics on a particular example. $b$ is a universal microscopic-independent number, which in (2+1)d is related to the universal conductivity at the quantum phase transition. $b$ can be computed exactly for certain transitions using the dualities between (2+1)d conformal field theories developed in recent years. We also compute the "strange correlator" of $O_\mathcal{C}$: $S_{\mathcal{C}} = \langle 0 | O_\mathcal{C} | 1 \rangle / \langle 0 | 1 \rangle$ where $|0\rangle$ and $|1\rangle$ are many-body states with different topological nature.

cond-mat.str-el↗

arXiv2021

Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the "tensor symmetry". We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the 't Hooft anomaly for the general Hamiltonians after "gauging" the dual generalized symmetries. A 3d system with dual anomalous 1-form symmetries can be viewed as the boundary of a 4d generalized symmetry protected topological (SPT) state with 1-form symmetries. We also present a prototype example of 4d SPT state with mixed 1-form and 0-form symmetry topological response theory as well as its physical construction. The boundary of this SPT state can be a 3d anomalous QED state, or an anomalous 1-form symmetry enriched topological order. Insights are gained by dimensional compatification/reduction. After dimensional compactification, the 3d system with N pairs of dual 1-form symmetries reduces to a 1d system with 2N pairs of dual U(1) global symmetries, which is the boundary of an ordinary 2d SPT state; while the 3d system with the tensor symmetry reduces to a 1d Lifshitz theory, which is protected by the center of mass conservation of the system.

cond-mat.str-el↗

arXiv2020

Continuous Néel-VBS Quantum Phase Transition in Non-Local one-dimensional systems with SO(3) Symmetry

One dimensional $(1d)$ interacting systems with local Hamiltonians can be studied with various well-developed analytical methods. Recently novel $1d$ physics was found numerically in systems with either spatially nonlocal interactions, or at the $1d$ boundary of $2d$ quantum critical points, and the critical fluctuation in the bulk also yields effective nonlocal interactions at the boundary. This work studies the edge states at the $1d$ boundary of $2d$ strongly interacting symmetry protected topological (SPT) states, when the bulk is driven to a disorder-order phase transition. We will take the $2d$ Affleck-Kennedy-Lieb-Tasaki (AKLT) state as an example, which is a SPT state protected by the SO(3) spin symmetry and spatial translation. We found that the original $(1+1)d$ boundary conformal field theory of the AKLT state is unstable due to coupling to the boundary avatar of the bulk quantum critical fluctuations. When the bulk is fixed at the quantum critical point, within the accuracy of our expansion method, we find that by tuning one parameter at the boundary, there is a generic direct transition between the long range antiferromagnetic Néel order and the valence bond solid (VBS) order. This transition is very similar to the Néel-VBS transition recently found in numerical simulation of a spin-1/2 chain with nonlocal spatial interactions. Connections between our analytical studies and recent numerical results concerning the edge states of the $2d$ AKLT-like state at a bulk quantum phase transition will also be discussed.

cond-mat.str-el↗

arXiv2020

Categorical Symmetries at Criticality

We study the concept of "categorical symmetry" introduced recently, which in the most basic sense refers to a pair of dual symmetries, such as the Ising symmetries of the $1d$ quantum Ising model and its self-dual counterpart. In this manuscript we study discrete categorical symmetry at higher dimensional critical points and gapless phases. At these selected gapless states of matter, we can evaluate the behavior of categorical symmetries analytically. We analyze the categorical symmetry at the following examples of criticality: (1) Lifshit critical point of a $(2+1)d$ quantum Ising system; (2) $(3+1)d$ photon phase as an intermediate gapless phase between the topological order and the confined phase of 3d $Z_2$ quantum gauge theory; (3) $2d$ and $3d$ examples of systems with both categorical symmetries (either 0-form or 1-form categorical symmetries) and subsystem symmetries. We demonstrate that at some of these gapless states of matter the categorical symmetries have very different behavior from the nearby gapped phases.

cond-mat.str-el↗

arXiv2020

Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications

We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d boundary state of 4d SPT states involving 1-form symmetries can be either a gapless photon phase (quantum electrodynamics) or gapped topological order enriched by 1-form symmetries, namely the loop excitations of these topological orders carry nontrivial 1-form symmetry charges. This study also serves the purpose of diagnosing anomaly of 3d states of matter. Connection between SPT states with 1-form symmetries and condensed matter systems such as quantum dimer models at one lower dimension will also be discussed. Whether a quantum dimer model can have a trivial gapped phase or not depends on the nature of its corresponding bulk state in one higher dimension.

cond-mat.str-el↗

arXiv2020

Orbital Orders and non-Fermi Liquid in Moiré systems

Motivated by recent observation of nematicity in Moiré systems, we study three different orbital orders that potentially can happen in Moiré systems: (1) the nematic order; (2) the valley polarization; and (3) the "compass order". Each order parameter spontaneously breaks part of the spatial symmetries of the system. We explore physics caused by the quantum fluctuations close to the order-disorder transition of these order parameters. Especially, we recognize that the symmetry of the Moiré systems leads to a crucial difference of the effective theory describing the nematic order from the standard Hertz-Millis formalism. We demonstrate that this key difference may lead to a special non-Fermi liquid behavior near the order-disorder nematic transition, different from the standard non-Fermi liquid behavior usually expected when a Fermi surface is coupled to the critical fluctuations of orbital orders. We also discuss the interplay of the three order parameters and the possible rich phase diagram at finite temperature. Within the three orbital orders, the valley polarization and the "compass order" likely strongly compete with the superconductor.

cond-mat.str-el↗

arXiv2020

Non-Landau Quantum Phase Transitions and nearly-Marginal non-Fermi Liquid

Non-fermi liquid and unconventional quantum critical points (QCP) with strong fractionalization are two exceptional phenomena beyond the classic condensed matter doctrines, both of which could occur in strongly interacting quantum many-body systems. This work demonstrates that using a controlled method one can construct a non-Fermi liquid within a considerable energy window based on the unique physics of unconventional QCPs. We will focus on the "nearly-marginal non-Fermi liquid", defined as a state whose fermion self-energy scales as $Σ_f(i ω) \sim i \mathrm{sgn}(ω)|ω|^α$ with $α$ close to $1$ in a considerable energy window. The nearly-marginal non-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 Landau phase transitions, for example the Wilson-Fisher fixed points. The fact that $η\sim 1$ justifies a perturbative renormalization group calculation proposed earlier. Various candidate QCPs that meet this desired condition are proposed.

cond-mat.str-el↗

arXiv2020

Topological Edge and Interface states at Bulk disorder-to-order Quantum Critical Points

We study the interplay between two nontrivial boundary effects: (1) the two dimensional ($2d$) edge states of three dimensional ($3d$) strongly interacting bosonic symmetry protected topological states, and (2) the boundary fluctuations of $3d$ bulk disorder-to-order phase transitions. We then generalize our study to $2d$ gapless states localized at an interface embedded in a $3d$ bulk, when the bulk undergoes a quantum phase transition. Our study is based on generic long wavelength descriptions of these systems and controlled analytic calculations. Our results are summarized as follows: ($i.$) The edge state of a prototype bosonic symmetry protected states can be driven to a new fixed point by coupling to the boundary fluctuations of a bulk quantum phase transition; ($ii.$) the states localized at a $2d$ interface of a $3d$ SU(N) quantum antiferromagnet may be driven to a new fixed point by coupling to the bulk quantum critical modes. Properties of the new fixed points identified are also studied.

cond-mat.str-el↗

arXiv2020

Boundary Criticality of Topological Quantum Phase Transitions in $2d$ systems

We discuss the boundary critical behaviors of two dimensional quantum phase transitions with fractionalized degrees of freedom in the bulk, motivated by the fact that usually it is the $1d$ boundary that is exposed and can be conveniently probed in many experimental platforms. In particular, we mainly discuss boundary criticality of two examples: i. the quantum phase transition between a $2d$ $Z_2$ topological order and an ordered phase with spontaneous symmetry breaking; ii. the continuous quantum phase transition between metal and a particular type of Mott insulator (U(1) spin liquid). This theoretical study could be relevant to many purely $2d$ systems, where recent experiments have found correlated insulator, superconductor, and metal in the same phase diagram.

cond-mat.str-el↗

arXiv2019

Emergent Fermi surface in a triangular-lattice SU(4) quantum antiferromagnet

Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group (DMRG) method, which we support with a field theory analysis.

cond-mat.str-el↗