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Cenke Xu

Publications and source records attributed to Cenke Xu.

At least 37 records · Page 2Linked to original sources
arXiv2024

Extracting subleading corrections in entanglement entropy at quantum phase transitions

We systematically investigate the finite size scaling behavior of the Rényi entanglement entropy (EE) of several representative 2d quantum many-body systems between a subregion and its complement, with smooth boundaries as well as boundaries with corners. In order to reveal the subleading correction, we investigate the quantity ``subtracted EE" $S^s(l) = S(2l) - 2S(l)$ for each model, which is designed to cancel out the leading perimeter law. We find that $\mathbf{(1)}$ for a spin-1/2 model on a 2d square lattice whose ground state is the Neel order, the coefficient of the logarithmic correction to the perimeter law is consistent with the prediction based on the Goldstone modes; $\mathbf{(2)}$ for the $(2+1)d$ O(3) Wilson-Fisher quantum critical point (QCP), realized with the bilayer antiferromagnetic Heisenberg model, a logarithmic subleading correction exists when there is sharp corner of the subregion, but for subregion with a smooth boundary our data suggests the absence of the logarithmic correction to the best of our efforts; $\mathbf{(3)}$ for the $(2+1)d$ SU(2) J-Q$_2$ and J-Q$_3$ model for the deconfined quantum critical point (DQCP), we find a logarithmic correction for the EE even with smooth boundary.

cond-mat.str-el↗
arXiv2024

Superconductor-Insulator Transition in the TMD moiré systems and the Deconfined Quantum Critical Point

We propose that the recently observed superconductor-insulator transition (SIT) in the twisted bilayer transition metal dichalcogenides moiré system at hole filling $ν= 1$ may be described by the deconfined quantum critical point (DQCP), which was originally proposed for the transition between the Néel order and the valence bond solid (VBS) order on the square lattice. The key symmetries involved in the original DQCP include a $\mathrm{SO}(3)_s$ spin symmetry, as well as a $C_4$ lattice rotation symmetry for the VBS order that is enlarged into a $\mathrm{U}(1)_v$ symmetry near the DQCP. In the current SIT under consideration, the counterpart of the $\mathrm{SO}(3)_s$ spin symmetry is an approximate $\mathrm{SO}(3)_v$ symmetry that transforms between different crystalline orders on the triangular lattice; and the role of the $\mathrm{U}(1)_v$ symmetry is replaced by the ordinary charge-$\mathrm{U}(1)_e$ symmetry. And at the DQCP the $\mathrm{SO}(3)_v \times \mathrm{U}(1)_e$ may enlarge into an emergent $\mathrm{SO}(5)$ symmetry. Under strain, the SIT is driven into either a prominent first order transition, or an "easy-plane" DQCP, which is expected to have an emergent $\mathrm{O}(4)$ symmetry.

cond-mat.str-el↗
arXiv2024

Pristine and Pseudo-gapped Boundaries of the Deconfined Quantum Critical Points

Bulk topology and criticality can both lead to nontrivial boundary effects. Topological orders are often characterized by their robust edge states, while bulk critical points can have different boundary scalings governed by boundary conditions. The interplay between these two different boundary effects is an intriguing problem. The boundary of the deconfined quantum critical point (DQCP) is the ideal platform for the interplay of the two boundary effects, as the DQCP is also an intrinsically gapless symmetry protected topological (igSPT) state. In this work we discuss the boundary of several analogues of the DQCP. We demonstrate that the fluctuation of the bulk order parameters and their various boundary conditions lead to a rich possibility of the edge states, including a "pseudogap" (or super power-law decay) behavior. We also discuss the quantum information perspective of our work, i.e. the implication of our results on DQCP under weak-measurement. Weak-measurement followed by post-selection can change the boundary condition at the temporal boundary in the path-integral representation of a density matrix, which will lead to different behaviors of the "strange correlator".

cond-mat.str-el↗
arXiv2024

Higher-form Symmetries under Weak Measurement

We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions, a phase transition can be driven by weak measurements, which suppresses the spontaneous breaking of the 1-form symmetry and weakens the 1-form symmetry charge fluctuation. We analyze the nature of the transitions employing the tool of duality, and we demonstrate that some of the transitions driven by weak measurement enjoy a line of fixed points with self-duality.

cond-mat.str-el↗
arXiv2024

Tunable exciton valley-pseudospin orders in moiré Bose-Hubbard model

Spin and charge are the two most important degrees of freedom of electrons. Their interplay lies at the heart of numerous strongly correlated phenomena including Hubbard model physics and high temperature superconductivity. Such interplay for bosons, on the other hand, is largely unexplored in condensed matter systems. Here we demonstrate a unique realization of the spin-1/2 Bose-Hubbard model through excitons in a semiconducting moiré superlattice. We find evidence of a transient in-plane ferromagnetic (FM-$xy$) order of exciton spin - here valley pseudospin - around exciton filling $ν_{ex}$ = 1, which transitions into a FM-$z$ order both with increasing exciton filling and a small magnetic field of 10 mT. The phase diagram is different from the fermion case and is qualitatively captured by a simple phenomenological model, highlighting the unique consequence of Bose-Einstein statistics. Our study paves the way for engineering exotic phases of matter from spinor bosons, as well as for unconventional devices in optics and quantum information science.

cond-mat.mes-hall↗
arXiv2024

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT.

cond-mat.str-el↗
arXiv2023

Boundary states of Three Dimensional Topological Order and the Deconfined Quantum Critical Point

We study the boundary states of the archetypal three-dimensional topological order, i.e. the three-dimensional $\mathbb{Z}_2$ toric code. There are three distinct elementary types of boundary states that we will consider in this work. In the phase diagram that includes the three elementary boundaries there may exist a multi-critical point, which is captured by the so-called deconfined quantum critical point (DQCP) with an "easy-axis" anisotropy. Moreover, there is an emergent $\mathbb{Z}_{2,\text{d}}$ symmetry that swaps two of the boundary types, and it becomes part of the global symmetry of the DQCP. The emergent $\mathbb{Z}_{2,\text{d}}$ symmetry on the boundary is originated from a type of surface defect in the bulk. We further find a gapped boundary with a surface topological order that is invariant under the emergent symmetry.

cond-mat.str-el↗
arXiv2023

The Conjugate Composite Fermi Liquid

Recent experimental observations of the fractional quantum anomalous Hall effect in spin/valley polarized moiré systems call for a more expansive theoretical exploration of strongly correlated physics in partially filled topological bands. In this work we study a state that we refer to as the conjugate-composite Fermi liquid (cCFL), which arises when a pair of Chern bands with opposite Chern numbers are both half-filled. We demonstrate that the cCFL is the parent state of various interesting phenomena. As an example, we demonstrate that with the existence of an inplane spin order, the cCFL could be driven into a quantum bad metal phase, in the sense that it is a metallic phase whose zero temperature longitudinal resistivity is finite, but far greater than the Mott-Ioffe-Regal limit, i.e. $ρ^e_{xx} \gg h/e^2$. The bad metal phase is also accompanied with a new Wiedemann-Franz law, meaning the thermal conductivity is proportional to the electrical resistivity rather than conductivity. Other proximate phases of the cCFL such as superconductivity and a chiral spin liquid phase can occur when the composite fermions (CF) form the inter-valley CF-exciton condensate.

cond-mat.str-el↗
arXiv2023

Decoherence through Ancilla Anyon Reservoirs

We explore the decoherence of the gapless/critical boundary of a topological order, through interactions with the bulk reservoir of "ancilla anyons." We take the critical boundary of the $2d$ toric code as an example. The intrinsic nonlocal nature of the anyons demands the strong and weak symmetry condition for the ordinary decoherence problem be extended to the strong or weak gauge invariance conditions. We demonstrate that in the $\textit{doubled}$ Hilbert space, the partition function of the boundary is mapped to two layers of the $2d$ critical Ising model with an inter-layer line defect that depends on the species of the anyons causing the decoherence. The line defects associated with the tunneling of bosonic $e$ and $m$ anyons are relevant, and result in long-range correlations for either the $e$ or $m$ anyon respectively on the boundary in the doubled Hilbert space. In contrast, the defect of the $f$ anyon is marginal and leads to a line of fixed points with varying effective central charges, and power-law correlations having continuously varying scaling dimensions. We also demonstrate that decoherence-analogues of Majorana zero modes are localized at the spatial interface of the relevant $e$ and $m$ anyon decoherence channels, which leads to a universal logarithmic scaling of the Rényi entropy of the boundary.

cond-mat.str-el↗
arXiv2023

Intertwined fractional quantum anomalous Hall states and charge density waves

Motivated by the recent experimental breakthrough on the observation of the fractional quantum anomalous Hall (FQAH) effects in semiconductor and graphene moiré materials, we explore the rich physics associated with the coexistence of FQAH effect and the charge density wave (CDW) order that spontaneously breaks the translation symmetry. We refer to a state with both properties as "FQAH-crystal". We show that the interplay between FQAH effect and CDW can lead to a rich phase diagram including multiple topological phases and topological quantum phase transitions at the same moiré filling. In particular, we demonstrate the possibility of direct quantum phase transitions from a FQAH-crystal with Hall conductivity $σ_H = - 2/3$ to a trivial CDW insulator with $σ_H = 0$, and more interestingly, to a QAH-crystal with $σ_H= -1$.

cond-mat.str-el↗
arXiv2023

Nonlinear Lifshitz Photon Theory in Condensed Matter Systems

We present an interacting theory of a $U(1)$ gauge boson with a quadratic dispersion relation, which we call the "nonlinear Lifshitz photon theory.'' The Lifshitz photon is a three-dimensional generalization of the Tkachenko mode in rotating superfluids. Starting from the Wigner crystal of charged particles coupled to a dynamical $U(1)$ gauge field, after integrating out gapped degrees of freedom, we arrive at the Lagrangian for the nonlinear Lifshitz photon. The symmetries of the theory include a global $U(1)$ 1-form symmetry and nonlinearly realized "magnetic" translation and rotation symmetries. The interaction terms in the theory lead to the decay of the Lifshitz photon, the rate of which we estimate. We show that the Wilson loop, which plays the role of the order parameter of the spontaneous breaking of the 1-form global symmetry, deviates from the perimeter law by an additional logarithmic factor. We explore potential connections to other condensed matter systems, with a particular focus on quantum spin ice and ferromagnets. Finally, we generalize our theory to higher dimensions.

cond-mat.str-el↗
arXiv2023

Quantum criticality under decoherence or weak measurement

Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCP) in a nontrivial way. As was pointed out in recent literature on $(1+1)d$ conformal field theory (CFT), the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without post-selecting the measurement outcomes. Our main results are: (1) for an O(N) Wilson-Fisher QCP under weak measurement with post-selection, an observer would in general observe two different types of boundary/defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic "extraordinary-log" correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no post-selection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the "disorder operator" would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.

cond-mat.stat-mech↗
arXiv2023

A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions

We argue that the chiral $U(1)_A$ symmetry of a Weyl fermion cannot be implemented by a shallow depth quantum circuit operation in a fermionic lattice Hamiltonian model with finite dimensional onsite Hilbert spaces. We also extend this result to discrete ${\mathbb{Z}}_{2N}$ subgroups of $U(1)_A$, in which case we show that for $N_f$ Weyl fermions of the same helicity, this group action cannot be implemented with shallow depth circuits when $N_f$ is not an integer multiple of $2N$.

cond-mat.str-el↗
arXiv2023

Conformal Field Theories generated by Chern Insulators under Quantum Decoherence

We demonstrate that the fidelity between a pure state trivial insulator and the mixed state density matrix of a Chern insulator under decoherence can be mapped to a variety of two-dimensional conformal field theories (CFT); more specifically, the quantity $\mathcal{Z} = \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the partition function of the desired CFT, where $\hatρ^D_c$ and $\hatρ_Ω$ are respectively the density matrices of the decohered Chern insulator and a pure state trivial insulator. For a pure state Chern insulator with Chern number $2N$, the fidelity $\mathcal{Z}$ is mapped to the partition function of the $\text{U}(2N)_1$ CFT; under weak decoherence, the Chern insulator density matrix can experience certain instability, and the "partition function" $\mathcal{Z}$ can flow to other interacting CFTs with smaller central charges. The Rényi relative entropy $\mathcal{F} = - \log \text{tr}\{ \hatρ^D_c \hatρ_Ω\}$ is mapped to the free energy of the CFT, and we demonstrate that the central charge of the CFT can be extracted from the finite size scaling of $\mathcal{F}$, analogous to the well-known finite size scaling of $2d$ CFT.

cond-mat.str-el↗
arXiv2022

Loops in 4+1d Topological Phases

2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form $\mathbb{Z}_2$ gauge field (the loop only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self `exchange' statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The $SL(2,\mathbb{Z}_2)$ symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the `fractional Maxwell theory' and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the $\mathbb{Z}_2$ gauge group to $\mathbb{Z}_N$.

cond-mat.str-el↗
arXiv2022

Vortex Fermi Liquid and Strongly Correlated Quantum Bad Metal

The semiclassical description of two-dimensional ($2d$) metals based on the quasiparticle picture suggests that there is a universal threshold of the resistivity: the resistivity of a $2d$ metal is bounded by the so called Mott-Ioffe-Regal (MIR) limit, which is at the order of $h/e^2$. If a system remains metallic while its resistivity is beyond the MIR limit, it is referred to as a "bad metal", which challenges our theoretical understanding as the very notion of quasiparticles is invalidated. The description of the system becomes even more challenging when there is also strong correlation between the electrons. Partly motivated by the recent experiment on transition metal dichalcogenides moiré heterostructure, we seek for understanding of strongly correlated bad metals whose resistivity far exceeds the MIR limit. For some strongly correlated bad metals, though a microscopic description based on electron quasiparticles fails, a tractable dual description based on the "vortex of charge" is still possible. We construct a concrete example of such strongly correlated bad metals where vortices are fermions with a Fermi surface, and we demonstrate that its resistivity can be exceptionally large at zero temperature. And when extra charge $δn_e$ is doped into the system away from half-filling, a small Drude weight proportional to $(δn_e)^2$ will emerge in the optical conductivity .

cond-mat.str-el↗
arXiv2022

Deconfined Quantum Critical Point with Non-locality

The deconfined quantum critical point (DQCP) between the Néel and valence bond solid (VBS) order was originally proposed in quantum spin systems with a local Hamiltonian. In the last few years analogues of DQCPs with nonlocal interactions have been explored, which can lead to rich possibilities. The nonlocal interactions can either arise from an instantaneous long range interaction in the Hamiltonian, or from gapless modes that reside in one higher spatial dimension. Here we consider another mechanism of generating nonlocal interactions by coupling the DQCP to the "hot spots" of a Fermi surface. We demonstrate that at least within a substantial energy window, the physics of the DQCP is controlled by a new fixed point with dynamical exponent $z > 1$

cond-mat.str-el↗
arXiv2022

Metal-Insulator Transition with Charge Fractionalization

It has been proposed that an extended version of the Hubbard model which potentially hosts rich correlated physics may be well simulated by the transition metal dichalcogenide (TMD) moiré heterostructures. Motivated by recent reports of continuous metal-insulator transition (MIT) at half filling, as well as correlated insulators at various fractional fillings in TMD moiré heterostructures, we propose a theory for the potentially continuous MIT with fractionalized electric charges. The charge fractionalization at the MIT will lead to various experimental observable effects, such as a large critical resistivity as well as large universal resistivity jump at the continuous MIT. These predictions are different from previously proposed theory for interaction-driven continuous MIT. Physics in phases near the MIT will also be discussed.

cond-mat.str-el↗