arXiv subjects

Yizhi You

Publications and source records attributed to Yizhi You.

54 records · Page 3Linked to original sources

arXiv2018

Higher order topological superconductors as generators of quantum codes

We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSC realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSC protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSC and topologically ordered phase.

cond-mat.str-el↗

arXiv2018

Classification of subsystem symmetry-protected topological phases

We consider symmetry-protected topological (SPT) phases in 2D protected by linear subsystem symmetries, i.e. those that act along rigid lines. There is a distinction between a "strong" subsystem SPT phase, and a "weak" one, which is composed of decoupled 1D SPTs with global symmetries. We propose a natural definition for strong equivalence of such phases, in terms of a linearly-symmetric local unitary transformation, under which a weak subsystem SPT is equivalent to the trivial phase. This leads to a number of distinct equivalence classes of strong subsystem SPTs, which we show are in one-to-one correspondence with elements of the group $\mathcal{C}[G_s] = \mathcal{H}^{2}[G_s^2,U(1)]/(\mathcal{H}^{2}[G_s,U(1)])^3$, where $G_s$ is the finite abelian onsite symmetry group. We also show that strong subsystem SPTs by our classification necessarily exhibit a spurious topological entanglement entropy on a cylinder.

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arXiv2018

Fractal Symmetric Phases of Matter

We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach. Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge. Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry. In 3D, our construction leads additionally to FSPT phases protected by higher form fractal symmetries and fracton topologically ordered phases enriched by the additional fractal symmetries.

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arXiv2018

Higher order symmetry-protected topological states for interacting bosons and fermions

Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges. Here, we explore symmetry protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher order symmetry protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the non-trivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.

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arXiv2018

Symmetric Fracton Matter: Twisted and Enriched

In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that these can realize subsystem symmetry protected topological phases with gapless boundary modes. Gauging the planar subsystem symmetry leads to a fracton order in which particles restricted to move along lines exhibit a new type of statistical interaction that is specific to the lattice geometry. We show that both the gapless boundary modes of the ungauged theory, and the statistical interactions after gauging, are naturally captured by a higher-rank version of Chern-Simons theory. We also show that gauging only part of the subsystem symmetry can lead to symmetry-enriched fracton orders, with quasiparticles carrying fractional symmetry charge.

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arXiv2018

Subsystem symmetry protected topological order

In this work, we introduce a new type of topological order which is protected by subsystem symmetries which act on lower dimensional subsets of lattice many-body system, e.g. along lines or planes in a three dimensional system. The symmetry groups for such systems exhibit a macroscopic number of generators in the infinite volume limit. We construct a set of exactly solvable models in $2d$ and $3d$ which exhibit such subsystem SPT (SSPT) phases with one dimensional subsystem symmetries. These phases exhibit analogs of phenomena seen in SPTs protected by global symmetries: gapless edge modes, projective realizations of the symmetries at the edge and non-local order parameters. Such SSPT phases are proximate, in theory space, to previously studied phases that break the subsystem symmetries and phases with fracton order which result upon gauging them.

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arXiv2017

Partial filled Landau Level at even denominator, a vortex metal with Berry phase

We develop a vortex metal theory for partial filled Landau Level at $ν=\frac{1}{2n}$, whose ground state contains a composite Fermi surface(FS) formed by the vortex of electrons. In the projected Landau Level limit, the composite Fermi surface contains $\frac{-π}{n}$ Berry phase. Such fractional Berry phase is a consequence of LL projection which produces the GMP guiding center algebra and embellishes an anomalous velocity to the equation of motion for the vortex metal. Further, we investigate a particle-hole symmetric bilayer system with $ν_1=\frac{1}{2n}$ and $ν_2=1-\frac{1}{2n}$ at each layer, and demonstrate that the $\frac{-π}{n}$ Berry phase on the composite Fermi surface leads to the suppression of $2k_f$ back-scattering between the PH partner bilayer, which could be a smoking gun to detect the fractional Berry phase. We also mention various instabilities and competing orders in such bilayer system including a $Z_{4n}$ topological order phase driven by quantum criticality.

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arXiv2017

Interlayer coherent composite Fermi liquid in Half-filled Landau Level bilayers, a window toward the hidden $π$ Berry phase

For interacting 2D electrons in the presence of magnetic field at half filling, the system forms a `composite Fermi liquid(CFL)' with emergent Fermi surface and exhibits metallic behavior, based on the standard Halperin, Lee, and Read(HLR) field theory. Recently, Son introduces a composite Dirac theory as the low energy effective description of Half-filled Landau Level. Such theory exhibits particle-hole symmetry and the underlying composite Fermi surface displays a robust $π$ Berry phase. In this paper, we start from the bilayer Half-filled Landau Level system where the two composite Fermi surface acquires interlayer coherence and forms bonding/anti-bonding composite fermi sea. The corresponding interlayer coherent composite Fermi liquid(ICCFL) phase provides a straightforward landscape to verify the Dirac nature in Son's theory and extract the hidden Berry phase structure of the composite Fermi surface. The ICCFL phase contains two Fermi surfaces which are detached in most regions but adhesive at two hot spots. Such nematic structure is a consequence of the Berry phase encoded in the Dirac Fermi surface which is absent in HLR theory. Due to the nematicity in ICCFL, the system supports half-quantum vortex with deconfined $\fracπ{2}$ gauge flux and the phase transition toward ICCFL contains a Lifshitz criticality with $z=3$ dynamical exponent. In addition, the exciton order parameter carries topological spin number so the ICCFL contains a unique Wen-Zee term which connects EM response with the background geometry curvature.

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arXiv2016

Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals

We investigate the unconventional quantum phase transitions in Weyl semimetals. The emergent boson fields, coupling with the Weyl fermion bilinears, contain a Wess-Zumino-Witten term or topological $Θ$ term inherited from the momentum space monopoles carried by Weyl points. Three types of unconventional quantum critical points will be studied in order: (1) The transition between two distinct symmetry breaking phases whose criticality is beyond Landau's paradigm. (2) The transition between a symmetry breaking state to a topological ordered state. (3) The transition between $3d$ topological order phase to trivial disordered phase whose criticality could be traced back to a $Z_2$ symmetry breaking transition in $4d$. The essence of these unconventional critical points lies in the fact that the topological defect of an order parameter carries either a nontrivial quantum number or a topological term so the condensation of the defects would either break some symmetry or give rise to a topological order phase with nontrivial braiding statistics.

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arXiv2016

Geometry defects in Bosonic symmetry protected topological phases

In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry protected topological(SPT) phases. We start from eight copies of 3D time-reversal($\mathcal{T}$) invariant topological superconductors(TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid crystal(TCL). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the $\mathcal{T}$ and translation invariant surface state is a double $[e\mathcal{T}m\mathcal{T}]$ state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in 2D boson SPT state described by an $O(4)$ non-linear $σ$-model(NL$σ$M) with topological $Θ$-term. By dressing the $O(4)$ vector with spiral order and gauge the symmetry, the dislocation has mutual semion statistics with the gauge flux. Further reduce the $O(4)$ NL$σM$ to the Ising limit, we arrive at the Levin-Gu model with stripy modulation whose dislocation has nontrivial braiding statistics.

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arXiv2016

Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings

In this paper, we investigate the theory of dynamical axion string emerging from chiral symmetry breaking in three-dimensional Weyl semimetals. The chiral symmetry is spontaneously broken by a charge density wave (CDW) order which opens an energy gap and converts the Weyl semimetal into an axion insulator. Indeed, the phase fluctuations of the CDW order parameter act as a dynamical axion field $θ({\vec{x}},t)$ and couples to electromagnetic field via $\mathcal{L}_θ=\frac{θ(\vec{x},t)}{32π^2} ε^{στνμ} F_{στ} F_{νμ}.$ Additionally, when the axion insulator is coupled to the background geometry/strain fields via torsional defects, i.e., screw dislocations, there is a novel interplay between the crystal dislocations and dynamical axion strings (i.e., vortices of the CDW order parameter). For example, the screw dislocation traps axial charge, and there is a Berry phase accumulation when an axion string is braided with a screw dislocation. In addition, a cubic coupling between the axial current and the geometry fields is non-vanishing and indicates a Berry phase accumulation during a particular three-loop braiding procedure where a dislocation loop is braided with another dislocation and they are both threaded by an axion string. We also observe a chiral magnetic effect induced by a screw dislocation density in the absence of chemical potential imbalance between Weyl points and describe an additional chiral geometric effect and a geometric Witten effect.

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arXiv2016

Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective field theory for the isotropic-nematic phase transition has $z = 3$ dynamical exponent due to Landau damping effects. We show that there is a Berry phase type term which governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a non-universal "Hall viscosity" of the dynamical metric. We show that the effective field theory has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the disclination of the nematic fluid, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.

cond-mat.str-el↗

arXiv2016

Stripe melting, a transition between weak and strong symmetry protected topological phases

For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong Symmetry Protected Topological (SPT) phases. A strong SPT phase is protected by the internal symmetry $G$ only while a weak SPT phase, fabricated by alignment of strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave(PDW) order in $2d$. We first demonstrate that the nodal line of the PDW contains a $1d$ boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in $2d$. The phase transition theory contains an O(4) non-linear-$σ$-model(NL$σ$M) with topological $Θ$-term emerging from the proliferation of domain walls bound to an SPT chain. Similar scheme also applies to weak-strong SPT transition in other dimensions and predicts possible phase transition from $2d$ to $3d$ topological order.

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arXiv2015

Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect

We consider the geometric part of the effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to the obtain correct gravitational linear response functions. In the lowest order in gradients the linear response generating functional includes Chern-Simons, Wen-Zee and gravitational Chern- Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

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arXiv2014

Theory of Nematic Fractional Quantum Hall State

We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall (FQH) states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has $z=2$ dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the non-dissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic FQH fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of Girvin-MacDonald-Platzman (GMP) mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn's theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid.

cond-mat.str-el↗

arXiv2014

Geometry of Fractional Quantum Hall Fluids

We use the field theory description of the fractional quantum Hall states to derive the universal response of these topological fluids to shear deformations and curvature of their background geometry, i.e. the Hall viscosity, the Wen-Zee term, and the gravitational Chern-Simons term. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry. We derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both abelian and non-abelian states.

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arXiv2014

Condensation of Lattice Defects and Melting Transitions in Quantum Hall phases

Motivated by recent progress in understanding the interplay between lattice and electronic topological phases, we consider quantum-melting transitions of {\it weak} quantum liquid crystals, a crystal and a nematic phase, in which electrons form a quantum Hall state. In certain classes of Chern band insulators and quantum Hall phases, it has been previously demonstrated that there are topological Chern-Simons terms such as a Hall viscosity term and a gravitational Chern-Simons term for local lattice deformations. The Chern-Simons terms can induce anyonic statistics for the topological lattice defects and furthermore dress the defects with certain symmetry quantum numbers. On the other hand, the melting transitions of such liquid-crystalline orders are driven by the condensation of lattice defects. Based on these observations, we show how the topological terms can change the nature of the proximate disordered phases of the quantum liquid crystalline phases. We derive and study the effective dual field theories for the liquid crystalline phases with the geometric Chern-Simons terms, and carefully examine the symmetry quantum numbers and statistics of defects. We show that a crystal may go through a continuous phase transition into another crystal with the new discrete translational symmetries because the dislocation, the topological defect in the crystal, carries non-zero crystal momentum due to the Hall viscosity term. For the nematic phase, the disclination will condense at the phase transition to the isotropic phase, and we show that the isotropic phase may support a deconfined fractionally charged excitation due to the Wen-Zee term, and thus the isotropic phase and the nematic phase have different electromagnetic Hall responses.

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arXiv2013

Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect

We derive from a microscopic model the effective theory of nematic order in a system with a spontaneous quantum anomalous Hall effect in two dimensions. Starting with a model of two-component fermions (a spinor field) with a quadratic band crossing and short range four-fermion marginally relevant interactions we use a 1/N expansion and bosonization methods to derive the effective field theory for the hydrodynamic modes associated with the conserved currents and with the local fluctuations of the nematic order parameter. We focus on the vicinity of the quantum phase transition from the isotropic Mott Chern insulating phase to a phase in which time-reversal symmetry breaking coexists with nematic order, the nematic Chern insulator. The topological sector of the effective field theory is a BF/Chern-Simons gauge theory. We show that the nematic order parameter field couples with the Maxwell-type terms of the gauge fields as the space components of a locally fluctuating metric tensor. The nematic field has $z=2$ dynamic scaling exponent. The low energy dynamics of the nematic order parameter is found to be governed by a Berry phase term. By means of a detailed analysis of the coupling of the spinor field of the fermions to the changes of their local frames originating from long-wavelength lattice deformations we calculate the Hall viscosity of this system and show that in this system is not the same as the Berry phase term in the effective action of the nematic field, but both are related to the concept of torque Hall viscosity which we introduce here.

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