arXiv subjects

Cenke Xu

Publications and source records attributed to Cenke Xu.

At least 91 records · Page 5Linked to original sources

arXiv2017

From Bosonic Topological Transition to Symmetric Fermion Mass Generation

The bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry protected topological phase and the trivial phase. In this work, we derive a description of this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ($N_f=4$). This allows us to describe the transition in a lattice model with the maximal microscopic symmetry: an internal SO(4) symmetry. Within a systematic renormalization group analysis, we identify the critical point with the desired O(4) emergent symmetry and all expected deformations. By lowering the microscopic symmetry we recover the previous $N_f=2$ non-compact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU(2) quantum chromodynamics-Higgs theory with $N_f=4$ flavors of SU(2) fundamental fermions and one SU(2) fundamental Higgs boson. This provides a consistency check on both theories.

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arXiv2017

Deconfined Quantum Critical Point on the Triangular Lattice

We first propose a topological term that captures the "intertwinement" between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" valence solid bond (VBS) order for spin-1/2 systems on a triangular lattice. Then using a controlled renormalization group calculation, we demonstrate that there exists an unfine-tuned direct continuous deconfined quantum critical point (dQCP) between the two ordered phases mentioned above. This dQCP is described by the $N_f = 4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/$Z_4$ symmetry only at the critical point. The topological term aforementioned is also naturally derived from the $N_f = 4 $ QED. We also point out that physics around this dQCP is analogous to the boundary of a $3d$ bosonic symmetry protected topological state with on-site symmetries only.

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arXiv2017

Emergent Symmetry and Tricritical Points near the deconfined Quantum Critical Point

Recent proposal of the duality between the $N=2$ noncompact QED$_3$ and the easy-plane noncompact CP$^1$ (NCCP$^1$) model suggests that the deconfined quantum critical point (dQCP) between the easy-plane antiferromagnet and the VBS order on the square lattice may have an emergent O(4) symmetry, due to the self-duality of the $N=2$ noncompact QED$_3$. Recent numerical progresses suggest that this easy-plane dQCP does exist and it has an emergent O(4) symmetry. But for the O(4) symmetry to really emerge at the dQCP, certain O(4) symmetry breaking perturbations need to be irrelevant at the putative O(4) fixed point. It is more convenient to study these symmetry breaking perturbations in the $N=2$ noncompact QED$_3$. We demonstrate that a natural large-$N$ generalization and a controlled $1/N$ expansion supports the stability of the O(4) fixed point against the symmetry breaking perturbations. We also develop the theory for two tricritical points close to the easy-plane dQCP. One tricritical point is between the dQCP and a {\it self-dual} $Z_2$ topological order; the other is the tricritical point that connects the continuous dQCP and a first order Néel-VBS transition, motivated by recent numerical results.

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arXiv2017

Duality between the deconfined quantum-critical point and the bosonic topological transition

Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.

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arXiv2017

Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase

We ask whether a local Hamiltonian with a featureless (fully gapped and nondegenerate) ground state could exist in certain quantum spin systems. We address this question by mapping the vicinity of certain quantum critical point (or gapless phase) of the $d-$dimensional spin system under study to the boundary of a $(d+1)-$dimensional bulk state, and the lattice symmetry of the spin system acts as an on-site symmetry in the field theory that describes both the selected critical point of the spin system, and the corresponding boundary state of the $(d+1)-$dimensional bulk. If the symmetry action of the field theory is nonanomalous, i.e. the corresponding bulk state is a trivial state instead of a bosonic symmetry protected topological (SPT) state, then a featureless ground state of the spin system is allowed; if the corresponding bulk state is indeed a nontrivial SPT state, then it likely excludes the existence of a featureless ground state of the spin system. From this perspective we identify the spin systems with SU($N$) and SO($N$) symmetries on one, two and three dimensional lattices that permit a featureless ground state. We also verify our conclusions by other methods, including an explicit construction of these featureless spin states.

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arXiv2017

Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems

We show that the out-of-time-order correlation (OTOC) $ \langle W(t)^\dagger V(0)^\dagger W(t)V(0)\rangle$ in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by the spectrum bifurcation renormalization group (SBRG). We find that in marginal MBL systems, the scrambling time $t_\text{scr}$ follows a stretched exponential scaling with the distance $d_{WV}$ between the operators $W$ and $V$: $t_\text{scr}\sim\exp(\sqrt{d_{WV}/l_0})$, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.

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arXiv2017

Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the chaotic non-Fermi liquid phase described by the ordinary $q = 4$ SYK model has marginally relevant/irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the SYK$_q$ model with a $q-$fermion interaction, similar perturbations can lead to a series of new interacting conformal field theory fixed points.

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arXiv2017

A model for continuous thermal Metal to Insulator Transition

We propose a $d-$dimensional interacting Majorana fermion model with quenched disorder, which gives us a continuous quantum phase transition between a diffusive thermal metal phase with a finite entropy density to an insulator phase with zero entropy density. This model is based on coupled Sachdev-Ye-Kitaev model clusters, and hence has a controlled large-$N$ limit. The metal-insulator transition is accompanied by a spontaneous time-reversal symmetry breaking. We perform controlled calculations to show that the diffusion constant jumps to zero discontinuously at the metal-insulator transition, while the time-reversal symmetry breaking order parameter increases continuously.

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arXiv2017

Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States

Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there is so far no successful experimental realization of any BSPT state in two or higher dimensions. In this paper, we propose that a two dimensional BSPT state with $U(1) \times U(1)$ symmetry can be realized in bilayer graphene in a magnetic field. Here the two $U(1)$ symmetries represent total spin $S^z$ and total charge conservation respectively. The Coulomb interaction plays a central role in this proposal -- it gaps out all the fermions at the boundary, so that only bosonic charge and spin degrees of freedom are gapless and protected at the edge. Based on the bosonic nature of the boundary states, we derive the bulk wave function for the bosonic charge and spin degrees of freedom, which takes exactly the same form as the desired BSPT state. We also propose that the bulk quantum phase transition between the BSPT and trivial phase, could become a "bosonic phase transition" with interactions. That is, only bosonic modes close their gap at the transition, which is fundamentally different from all the well-known topological insulator to trivial insulator transitions which occur for free fermion systems. We discuss various experimental consequences of this proposal.

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arXiv2017

Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry

We discuss three dimensional $Z_2$ topological phases enriched by the $Z_2^T$ time-reversal symmetry with bosonic bulk excitations. Some of these phases can be constructed by coupling the three dimensional symmetry protected topological phases with $Z_2 \times Z_2^T$ symmetry to a deconfined dynamical $Z_2$ gauge field. Besides these simple phases, we also construct a special root phase (phase 3) which cannot be interpreted as gauged $Z_2 \times Z_2^T$ SPT phase. The $2d$ boundary of these phases can have an extra $Z_2$ topological order in addition to their bulk topological order. In one of the possible boundary states of this special root phase (phase 3), $Z_2^T$ acts as the "self-dual" transformation of the boundary topological order, in the sense that the boundary $e$ and $m$ anyons are interchanged under $Z_2^T$.

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arXiv2016

Symmetry Protected Topological Hopf Insulator and its Generalizations

We study a class of $3d$ and $4d$ topological insulators whose topological nature is characterized by the Hopf map and its generalizations. We identify the symmetry $\mathcal{C}^\prime$, a generalized particle-hole symmetry that gives the Hopf insulator a $\mathbb{Z}_2$ classification. The $4d$ analogue of the Hopf insulator with symmetry $\mathcal{C}^\prime$ has the same $\mathbb{Z}_2$ classification. The minimal models for the $3d$ and $4d$ Hopf insulator can be heuristically viewed as "Chern-insulator$ \rtimes S^1$" and "Chern-insulator$\rtimes T^2$" respectively. We also discuss the relation between the Hopf insulator and the Weyl semimetals, which points the direction for its possible experimental realization.

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arXiv2016

Duality and bosonization of (2+1)d Majorana fermions

We construct a dual bosonized description of a massless Majorana fermion in $(2+1)d$. In contrast to Dirac fermions, for which a bosonized description can be constructed using a flux attachment procedure, neutral Majorana fermions call for a different approach. We argue that the dual theory is an $SO(N)_1$ Chern-Simons gauge theory with a critical $SO(N)$ vector bosonic matter field ($N \geq 3$). The monopole of the $SO(N)$ gauge field is identified with the Majorana fermion. We provide evidence for the duality by establishing the correspondence of adjacent gapped phases and by a parton construction. We also propose a generalization of the duality to $N_f$ flavors of Majorana fermions, and discuss possible resolutions of a caveat associated with an emergent global $Z_2$ symmetry. Finally, we conjecture a dual description of an $\mathcal{N} = 1$ supersymmetric fixed point in $(2+1)d$, which is realized by tuning a single flavor of Majorana fermions to an interacting (Gross-Neveu) critical point.

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arXiv2016

Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States

We consider the Sachdev-Ye-Kitaev (SYK) model as an effective theory arising at the zero-dimensional boundary of a many-body localized, Fermionic symmetry protected topological (SPT) phase in one spatial dimension. The Fermions at the boundary are always fully interacting. We find that the boundary is thermalized and investigate how its boundary anomaly, dictated by the bulk SPT order, is encoded in the quantum chaotic eigenspectrum of the SYK model. We show that depending on the SPT symmetry class, the boundary many-body level statistics cycle in a systematic manner through those of the three different Wigner-Dyson random matrix ensembles with a periodicity in the topological index that matches the interaction-reduced classification of the bulk SPT states. We consider all three symmetry classes BDI, AIII, and CII, whose SPT phases are classified in one spatial dimension by $\mathbb{Z}$ in the absence of interactions. For symmetry class BDI, we derive the eight-fold periodicity of the Wigner-Dyson statistics by using Clifford algebras.

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arXiv2016

Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model

Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the $(1+1)d$ boundary, before the bulk quantum phase transition to a topologically trivial phase. Therefore, finite fermion gaps both in the bulk and on the edge, together with the robust gapless bosonic edge modes, prove that our system becomes an emergent bosonic SPT phase at low energy, which is, for the first time, directly observed in an interacting fermion lattice model.

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arXiv2016

A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories

Using the duality between seemingly different (2+1)d conformal field theories (CFT) proposed recently, we study a series of (2+1)d stable self-dual interacting CFTs. These CFTs can be realized (for instance) on the boundary of the (3+1)d bosonic topological insulator protected by U(1) and time-reversal symmetry, and they remain stable as long as these symmetries are preserved. When realized as a boundary system, these CFTs can be driven into anomalous fractional quantum Hall states once time-reversal is broken. We demonstrate that the newly proposed dualities allow us to study these CFTs quantitatively through a controlled calculation, without relying on a large flavor number of matter fields.

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arXiv2016

"Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator

In the last few years a lot of exotic and anomalous topological phases were constructed by proliferating the vortex like topological defects on the surface of the $3d$ topological insulator (TI). In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortex like topological defects. In general we will discuss a $(2+1)d$ quantum phase transition described by the following field theory: $\mathcal{L} = \barψγ_μ(\partial_μ- i a_μ) ψ+ |(\partial_μ- i k a_μ)ϕ|^2 + r |ϕ|^2 + g |ϕ|^4$, with tuning parameter $r$, arbitrary integer $k$, Dirac fermion $ψ$ and complex scalar bosonic field $ϕ$ which both couple to the same $(2+1)d$ dynamical noncompact U(1) gauge field $a_μ$. The physical meaning of these quantities/fields will be explained in the text. We demonstrate that this quantum critical point has a quasi self-dual nature. And at this quantum critical point, various universal quantities such as the electrical conductivity, and scaling dimension of gauge invariant operators can be calculated systematically through a $1/k^2$ expansion, based on the observation that the limit $k \rightarrow + \infty$ corresponds to an ordinary $3d$ XY transition.

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arXiv2016

Interacting topological phases in thin films of topological mirror Kondo insulators

We study the interaction effects on thin films of topological mirror Kondo insulators (TMKI), where the strong interaction is expected to play an important role. Our study has led to the following results: (1) We identify a rich phase diagram of non-interacting TMKI with different mirror Chern numbers in the monolayer and bilayer thin films; (2) We obtain the phase diagram with interaction and identify the regimes of interaction parameters to mimic bosonic symmetry protected topological phases with either gapless bosonic modes or spontaneous mirror symmetry breaking at the boundary; (3) For the spontaneous mirror symmetry breaking boundary, we also study various domain-wall defects between different mirror symmetry breaking order parameters at the boundary. Our results reveal that the thin film TMKI serves as an intriguing platform for the experimental studies of interacting topological phases.

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arXiv2016

Stable Interacting (2 + 1)d Conformal Field Theories at the Boundary of a class of (3 + 1)d Symmetry Protected Topological Phases

Motivated by recent studies of symmetry protected topological (SPT) phases, we explore the possible gapless quantum disordered phases in the $(2+1)d$ nonlinear sigma model defined on the Grassmannian manifold $\frac{U(N)}{U(n)\times U(N - n)}$ with a Wess-Zumino-Witten (WZW) term at level $k$, which is the effective low energy field theory of the boundary of certain $(3+1)d$ SPT states. With $k = 0$, this model has a well-controlled large-$N$ limit, $i.e.$ its renormalization group equations can be computed exactly with large-$N$. However, with the WZW term, the large-$N$ and large-$k$ limit alone is not sufficient for a reliable study of the nature of the quantum disordered phase. We demonstrate that through a combined large-$N$, large-$k$ and $ε-$generalization, a stable fixed point in the quantum disordered phase can be reliably located in the large$-N$ limit and leading order $ε-$expansion, which corresponds to a $(2+1)d$ strongly interacting conformal field theory.

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