arXiv subjects

Chao-Ming Jian

Publications and source records attributed to Chao-Ming Jian.

At least 73 records · Page 4Linked to original sources

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

Emergent Superconductivity in the weak Mott insulator phase of bilayer Graphene Moiré Superlattice

We propose a phenomenological understanding of the recently discovered weak Mott insulator in the moiré superlattice of twisted bilayer graphene, especially the emergent superconductivity at low temperature within the weak Mott insulator phase, namely while lowering temperature, the longitudinal resistivity first grows below temperature $T_m$, but then rapidly drops to zero at even lower temperature $T_c$. An emergent superconductor in an insulator phase is very unusual. Here we propose that this phenomenon is due to the pure two-dimensional nature of the bilayer graphene moiré superlattice. We also compare our results with other theories proposed so far.

cond-mat.str-el↗

arXiv2018

Interacting Topological Insulators with Synthetic Dimensions

Recent developments of experimental techniques have given us unprecedented opportunities of studying topological insulators in high dimensions, while some of the dimensions are "synthetic", in the sense that the effective lattice momenta along these synthetic dimensions are controllable periodic tuning parameters. In this work, we study interaction effects on topological insulators with synthetic dimensions. We show that although the free fermion band structure of high dimensional topological insulators can be precisely simulated with the "synthetic techniques", the generic interactions in these effective synthetic topological insulators are qualitatively different from the local interactions in ordinary condensed matter systems. And we show that these special but generic interactions have unexpected effects on topological insulators, namely they would change (or reduce) the classification of topological insulators differently from the previously extensively studied local interactions.

cond-mat.str-el↗

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.

cond-mat.str-el↗

arXiv2017

Lattice Homotopy Constraints on Phases of Quantum Magnets

The Lieb-Schultz-Mattis (LSM) theorem and its extensions forbid trivial phases from arising in certain quantum magnets. Constraining infrared behavior with the ultraviolet data encoded in the microscopic lattice of spins, these theorems tie the absence of spontaneous symmetry breaking to the emergence of exotic phases like quantum spin liquids. In this work, we take a new topological perspective on these theorems, by arguing they originate from an obstruction to "trivializing" the lattice under smooth, symmetric deformations, which we call the "lattice homotopy problem." We conjecture that all LSM-like theorems for quantum magnets (many previously-unknown) can be understood from lattice homotopy, which automatically incorporates the full spatial symmetry group of the lattice, including all its point-group symmetries. One consequence is that any spin-symmetric magnet with a half-integer moment on a site with even-order rotational symmetry must be a spin liquid. To substantiate the claim, we prove the conjecture in two dimensions for some physically relevant settings.

cond-mat.str-el↗

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.

cond-mat.str-el↗

arXiv2017

A strongly correlated metal built from Sachdev-Ye-Kitaev models

Strongly correlated metals comprise an enduring puzzle at the heart of condensed matter physics. Commonly a highly renormalized heavy Fermi liquid occurs below a small coherence scale, while at higher temperatures a broad incoherent regime pertains in which quasi-particle description fails. Despite the ubiquity of this phenomenology, strong correlations and quantum fluctuations make it challenging to study. The Sachdev-Ye-Kitaev(SYK) model describes a $0+1$D quantum cluster with random all-to-all \emph{four}-fermion interactions among $N$ Fermion modes which becomes exactly solvable as $N\rightarrow \infty$, exhibiting a zero-dimensional non-Fermi liquid with emergent conformal symmetry and complete absence of quasi-particles. Here we study a lattice of complex-fermion SYK dots with random inter-site \emph{quadratic} hopping. Combining the imaginary time path integral with \emph{real} time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio $L\equiv \frac{κρ}{T}$ varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

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.

cond-mat.str-el↗

arXiv2017

Strongly Interacting Phases of Metallic Wires in Strong Magnetic Field

We investigate theoretically an interacting metallic wire with a strong magnetic field directed along its length and show that it is a new and highly tunable one-dimensional system. By considering a suitable change in spatial geometry, we map the problem in the zeroth Landau level with Landau level degeneracy $N$ to one-dimensional fermions with an $N$-component pseudospin degree of freedom and $SU(2)$-symmetric interactions. This mapping allows us to establish the phase diagram as a function of the interactions for small $N$ (and make conjectures for large $N$) using renormalization group and bosonization techniques. We find pseudospin-charge separation with a gapless $U(1)$ charge sector and several possible strong-coupling phases in the pseudospin sector. For odd $N$, we find a fluctuating pseudospin-singlet charge density wave phase and a fluctuating pseudospin-singlet superconducting phase which are topologically distinct. For even $N>2$, similar phases exist, although they are not topologically distinct, and an additional, novel pseudospin-gapless phase appears. We discuss experimental conditions for observing our proposals.

cond-mat.str-el↗

arXiv2016

Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies

We study symmetry-enriched topological (SET) phases in 2+1 space-time dimensions with spatial reflection and/or time-reversal symmetries. We provide a systematic construction of a wide class of reflection and time-reversal SET phases in terms of a topological path integral defined on general space-time manifolds. An important distinguishing feature of different topological phases with reflection and/or time-reversal symmetry is the value of the path integral on non-orientable space-time manifolds. We derive a simple general formula for the path integral on the manifold $Σ^2 \times S^1$, where $Σ^2$ is a two-dimensional non-orientable surface and $S^1$ is a circle. This also gives an expression for the ground state degeneracy of the SET on the surface $Σ^2$ that depends on the reflection symmetry fractionalization class, generalizing the Verlinde formula for ground state degeneracy on orientable surfaces. Consistency of the action of the mapping class group on non-orientable manifolds leads us to a constraint that can detect when a time-reversal or reflection SET phase is anomalous in (2+1)D and, thus, can only exist at the surface of a (3+1)D symmetry protected topological (SPT) state. Given a (2+1)D reflection and/or time-reversal SET phase, we further derive a general formula that determines which (3+1)D reflection and/or time-reversal SPT phase hosts the (2+1)D SET phase as its surface termination. A number of explicit examples are studied in detail.

cond-mat.str-el↗

arXiv2016

Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions

We calculate the topological part of the electromagnetic response of Bosonic Integer Quantum Hall (BIQH) phases in odd (spacetime) dimensions, and Bosonic Topological Insulator (BTI) and Bosonic chiral semi-metal (BCSM) phases in even dimensions. To do this we use the Nonlinear Sigma Model (NLSM) description of bosonic symmetry-protected topological (SPT) phases, and the method of gauged Wess-Zumino (WZ) actions. We find the surprising result that for BIQH states in dimension $2m-1$ ($m=1,2,\dots$), the bulk response to an electromagnetic field $A_μ$ is characterized by a Chern-Simons term for $A_μ$ with a level quantized in integer multiples of $m!$ (factorial). We also show that BTI states (which have an extra $\mathbb{Z}_2$ symmetry) can exhibit a $\mathbb{Z}_2$ breaking Quantum Hall effect on their boundaries, with this boundary Quantum Hall effect described by a Chern-Simons term at level $\frac{m!}{2}$. We show that the factor of $m!$ can be understood by requiring gauge invariance of the exponential of the Chern-Simons term on a general Euclidean manifold, and we also use this argument to characterize the electromagnetic and gravitational responses of fermionic SPT phases with $U(1)$ symmetry in all odd dimensions. We then use our gauged boundary actions for the BIQH and BTI states to (i) construct a bosonic analogue of a chiral semi-metal (BCSM) in even dimensions, (ii) show that the boundary of the BTI state exhibits a bosonic analogue of the parity anomaly of Dirac fermions in odd dimensions, and (iii) study anomaly inflow at domain walls on the boundary of BTI states. In a series of Appendices we derive important formulas and additional results. In particular, in Appendix A we use the connection between equivariant cohomology and gauged WZ actions to give a mathematical interpretation of the actions for the BIQH and BTI boundaries constructed in this paper.

cond-mat.str-el↗

arXiv2016

Featureless quantum insulator on the honeycomb lattice

We show how to construct fully symmetric, gapped states without topological order on a honey- comb lattice for S = 1/2 spins using the language of projected entangled pair states(PEPS). An explicit example is given for the virtual bond dimension D = 4. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking, and the existence of energy gap in the proposed wave functions, are checked by numerical calculations of the entanglement entropy and various correlation functions. Our work provides the first explicit realization of a featureless quantum insulator for spin-1/2 particles on a honeycomb lattice.

cond-mat.str-el↗

arXiv2015

Bulk Entanglement Spectrum in Gapped Spin Ladders

We study the bulk entanglement of a series of gapped ground states of spin ladders, representative of the Haldane phase. These ground states of spin $S/2$ ladders generalize the valence bond solid ground state. In the case of spin 1/2 ladders, we study a generalization of the Affleck-Kennedy-Lieb-Tasaki and Nersesyan-Tsvelik states and fully characterize the bulk entanglement Hamiltonian. In the case of general spin $S$ we argue that in the Haldane phase the bulk entanglement spectrum of a half integer ladder is either gapless or possess a degenerate ground state. For ladders with integer valued spin particles, the generic bulk entanglement spectrum should have an entanglement gap. Finally, we give an example of a series of trivial states of higher spin $S>1$ in which the bulk entanglement Hamiltonian is critical, signaling that the relation between topological states and a critical bulk entanglement Hamiltonian is not unique to topological systems.

cond-mat.str-el↗

arXiv2015

Long-range mutual information and topological uncertainty principle

Ordered phases in Landau paradigm can be diagnosed by a local order parameter, whereas topologically ordered phases cannot be detected in such a way. In this paper, we propose long-range mutual information(LRMI) as a unified diagnostic for both conventional long-range order and topological order. Using the LRMI, we characterize orders in $n+1$D gapped systems as $m$-membrane condensates with $ 0 \leq m \leq n-1$. The familiar conventional order and 2+1D topological orders are respectively identified as $0$-membrane and $1$-membrane condensates. We propose and study the topological uncertainty principle, which describes the non-commuting nature of non-local order parameters in topological orders.

cond-mat.str-el↗

arXiv2015

The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D

The peculiar features of quantum magnetism sometimes forbid the existence of gapped `featureless' paramagnets which are fully symmetric and unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a constraint, but it is not known what the most general restriction might be. We focus on the existence of featureless paramagnets on the spin-1 square lattice and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space group symmetries in 2+1D. Although featureless paramagnet phases are not ruled out by any existing theorem, field theoretic arguments disfavor their existence. Nevertheless, by generalizing the construction of Affleck, Kennedy, Lieb and Tasaki to a class we call `slave-spin' states, we propose featureless wave functions for these models. The featureless-ness of the spin-1 slave-spin states on the square and honeycomb lattice are verified both analytically and numerically, but the status of the spin-1/2 honeycomb state remains unclear.

cond-mat.str-el↗

arXiv2015

The almost mobility edge in the almost Mathieu equation

Harper's equation (aka the "almost Mathieu" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V E_c$, form a set of narrow bands with exponentially small bandwidths $ \sim t\ \exp[-(2πα/Q)]$ (where $α$ is an energy dependent number of order 1) separated by band-gaps $ \sim t Q$. Thus, the states with $|E|> E_c$ are "almost localized" in that they have an exponentially large effective mass and are easily localized by small perturbations. We establish this both using exact numerical solution of the problem, and by exploiting the well known fact that the same eigenvalue problem arises in the Hofstadter problem of an electron moving on a 2D lattice in the presence of a magnetic field, $B=Q/2π$. From the 2D perspective, the almost localized states are simply the Landau levels associated with semiclassical precession around closed contours of constant quasiparticle energy; that they are not truly localized reflects an extremely subtle form of magnetic breakdown.

cond-mat.mes-hall↗