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.

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation.

The "symmetric mass generation" (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. 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 conformal field theory.

A No-Go Result for Implementing Chiral Symmetries by Locality-Preserving Unitaries in a Three-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 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.

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 fractonlike models in standard condensed matter platforms is the creation of multispin 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.

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 introduced in Newman et al., [Phys. Rev. E 60, 5068 (1999).PLEEE81063-651X10.1103/PhysRevE.60.5068]. 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)/lnp. 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, is discussed.

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 method, which we support with a field theory analysis.

Topological Superconductivity in Twisted Multilayer Graphene.

We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat miniband resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of the preferred pairing states, favoring spin triplet d+id order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum hc/(4e), and have topologically protected gapless edge states.

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)×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 above conclusion, we propose that the bulk quantum phase transition between the BSPT and trivial phase, which can be driven by applying both magnetic and electric fields, can 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 that occur for free fermion systems. We discuss various experimental consequences of this proposal.

Wave function and strange correlator of short-range entangled states.

We demonstrate the following conclusion: If |Ψ⟩ is a one-dimensional (1D) or two-dimensional (2D) nontrivial short-range entangled state and |Ω⟩ is a trivial disordered state defined on the same Hilbert space, then the following quantity (so-called "strange correlator") C(r,r('))=⟨Ω|ϕ(r)ϕ(r('))|Ψ⟩/⟨Ω|Ψ⟩ either saturates to a constant or decays as a power law in the limit |r-r(')|→+∞, even though both |Ω⟩ and |Ψ⟩ are quantum disordered states with short-range correlation; ϕ(r) is some local operator in the Hilbert space. This result is obtained based on both field theory analysis and an explicit computation of C(r,r(')) for four different examples: 1D Haldane phase of spin-1 chain, 2D quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2D spin-2 Affleck-Kennedy-Lieb-Tasaki state on the square lattice, and the 2D bosonic symmetry-protected topological phase with Z(2) symmetry. This result can be used as a diagnosis for short-range entangled states in 1D and 2D.

Tunable exciton valley-pseudospin orders in moiré superlattices.

Excitons in two-dimensional (2D) semiconductors have offered an attractive platform for optoelectronic and valleytronic devices. Further realizations of correlated phases of excitons promise device concepts not possible in the single particle picture. Here we report tunable exciton "spin" orders in WSe2/WS2 moiré superlattices. We find evidence of an in-plane (xy) order of exciton "spin"-here, valley pseudospin-around exciton filling vex = 1, which strongly suppresses the out-of-plane "spin" polarization. Upon increasing vex or applying a small magnetic field of ~10 mT, it transitions into an out-of-plane ferromagnetic (FM-z) spin order that spontaneously enhances the "spin" polarization, i.e., the circular helicity of emission light is higher than the excitation. The phase diagram is qualitatively captured by a spin-1/2 Bose-Hubbard model and is distinct from the fermion case. Our study paves the way for engineering exotic phases of matter from correlated spinor bosons, opening the door to a host of unconventional quantum devices.

Nonperturbative effects of a topological theta term on principal chiral nonlinear sigma models in 2 + 1 dimensions.

We study the effects of a topological Theta term on 2+1-dimensional principal chiral models, which are nonlinear sigma models defined on Lie group manifolds. We find that when Θ=π, the nature of the disordered phase of the principal chiral model is strongly affected by the topological term: it is either a gapless conformal field theory, or it is gapped and twofold degenerate. The result of our Letter can be used to analyze the boundary states of three-dimensional symmetry protected topological phases.

Non-Fermi-liquid and topological states with strong spin-orbit coupling.

We argue that a class of strongly spin-orbit-coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by Coulomb interactions, a problem studied by Abrikosov and collaborators. It contains twofold degenerate conduction and valence bands touching quadratically at the zone center. Using modern renormalization group methods, we update and extend Abrikosov's classic work and show that interactions induce a quantum critical non-Fermi-liquid phase, stable provided time-reversal and cubic symmetries are maintained. We determine the universal power-law exponents describing various observables in this Luttinger-Abrikosov-Beneslavskii state, which include conductivity, specific heat, nonlinear susceptibility, and the magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes a topological insulator and Weyl semimetal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sublinearly with magnetization σ(xy)∼M0.51.

Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice.

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Evidence of frustrated magnetic interactions in a Wigner-Mott insulator.

Electrons in two-dimensional semiconductor moiré materials are more delocalized around the lattice sites than those in conventional solids1,2. The non-local contributions to the magnetic interactions can therefore be as important as the Anderson superexchange3, which makes the materials a unique platform to study the effects of competing magnetic interactions3,4. Here we report evidence of strongly frustrated magnetic interactions in a Wigner-Mott insulator at a two-thirds (2/3) filling of the moiré lattice in angle-aligned WSe2/WS2 bilayers. Magneto-optical measurements show that the net exchange interaction is antiferromagnetic for filling factors below 1 with a strong suppression at a 2/3 filling. The suppression is lifted on screening of the long-range Coulomb interactions and melting of the Wigner-Mott insulators by a nearby metallic gate. The results can be qualitatively captured by a honeycomb-lattice spin model with an antiferromagnetic nearest-neighbour coupling and a ferromagnetic second-neighbour coupling. Our study establishes semiconductor moiré materials as a model system for lattice-spin physics and frustrated magnetism5.

Topological quantum liquids with quaternion non-Abelian statistics.

Noncollinear magnetic order is typically characterized by a tetrad ground state manifold (GSM) of three perpendicular vectors or nematic directors. We study three types of tetrad orders in two spatial dimensions, whose GSMs are SO(3) = S(3)/Z(2), S(3)/Z(4), and S(3)/Q(8), respectively. Q(8) denotes the non-Abelian quaternion group with eight elements. We demonstrate that after quantum disordering these three types of tetrad orders, the systems enter fully gapped liquid phases described by Z(2), Z(4), and non-Abelian quaternion gauge field theories, respectively. The latter case realizes Kitaev's non-Abelian toric code in terms of a rather simple spin-1 SU(2) quantum magnet. This non-Abelian topological phase possesses a 22-fold ground state degeneracy on the torus arising from the 22 representations of the Drinfeld double of Q(8).

Spin liquid phases for spin-1 systems on the triangular lattice.

Motivated by recent experiments on material Ba3NiSb2O9, we propose two novel spin liquid phases (A and B) for spin-1 systems on a triangular lattice. At the mean field level, both spin liquid phases have gapless fermionic spinon excitations with quadratic band touching; thus, in both phases the spin susceptibility and γ=C(v)/T saturate to a constant at zero temperature, which are consistent with the experimental results on Ba3NiSb2O9. On the lattice scale, these spin liquid phases have Sp(4)~SO(5) gauge fluctuation, while in the long wavelength limit this Sp(4) gauge symmetry is broken down to U(1)×Z(2) in the type A spin liquid phase, and broken down to Z(4) in the type B phase. We also demonstrate that the A phase is the parent state of the ferroquadrupole state, nematic state, and the noncollinear spin density wave state.

Successive phase transitions and extended spin-excitation continuum in the S=1/2 triangular-lattice antiferromagnet Ba3CoSb2O9.

Using magnetic, thermal, and neutron measurements on single-crystal samples, we show that Ba3CoSb2O9 is a spin-1/2 triangular-lattice antiferromagnet with the c axis as the magnetic easy axis and two magnetic phase transitions bracketing an intermediate up-up-down phase in magnetic field applied along the c axis. A pronounced extensive neutron-scattering continuum above spin-wave excitations, observed below T(N), implies that the system is in close proximity to one of two spin-liquid states that have been predicted for a 2D triangular lattice.

High-pressure sequence of Ba3NiSb2O9 structural phases: new S = 1 quantum spin liquids based on Ni2+.

Two new gapless quantum spin-liquid candidates with S = 1 (Ni(2+)) moments: the 6H-B phase of Ba(3)NiSb(2)O(9) with a Ni(2+)-triangular lattice and the 3C phase with a Ni(2/3)Sb(1/3)-three-dimensional edge-shared tetrahedral lattice were obtained under high pressure. Both compounds show no magnetic order down to 0.35 K despite Curie-Weiss temperatures θ(CW) of -75.5 (6H-B) and -182.5 K (3C), respectively. Below ~25 K, the magnetic susceptibility of the 6H-B phase saturates to a constant value χ(0) = 0.013 emu/mol, which is followed below 7 K by a linear-temperature-dependent magnetic specific heat (C(M)) displaying a giant coefficient γ = 168 mJ/mol K(2). Both observations suggest the development of a Fermi-liquid-like ground state. For the 3C phase, the C(M) perpendicular T(2) behavior indicates a unique S = 1, 3D quantum spin-liquid ground state.

Majorana liquids: the complete fractionalization of the electron.

We describe ground states of correlated electron systems in which the electron fractionalizes into separate quasiparticles which carry its spin and its charge, and into real Majorana fermions which carry its Fermi statistics. Such parent states provide a unified theory of previously studied fractionalized states: their descendants include insulating and conducting states with neutral spin S=1/2 fermionic spinons, and states with spinless fermionic charge carriers. We illustrate these ideas on the honeycomb lattice, with field theories of such states and their phase transitions.

Gauge symmetry and non-Abelian topological sectors in a geometrically constrained model on the honeycomb lattice.

We study a constrained statistical-mechanical model in two dimensions that has three useful descriptions. They are (i) the Ising model on the honeycomb lattice, constrained to have three up spins and three down spins on every hexagon, (ii) the three-color and fully packed loop model on the links of the honeycomb lattice, with loops around a single hexagon forbidden, and (iii) three Ising models on interleaved triangular lattices, with domain walls of the different Ising models not allowed to cross. Unlike the three-color model, the configuration space on the sphere or plane is connected under local moves. On higher-genus surfaces there are infinitely many dynamical sectors, labeled by a noncontractible set of nonintersecting loops. We demonstrate that at infinite temperature the transfer matrix admits an unusual structure related to a gauge symmetry for the same model on an anisotropic lattice. This enables us to diagonalize the original transfer matrix for up to 36 sites, finding an entropy per plaquette S/k{B} approximately 0.3661 ... centered and substantial evidence that the model is not critical. We also find the striking property that the eigenvalues of the transfer matrix on an anisotropic lattice are given in terms of Fibonacci numbers. We comment on the possibility of a topological phase, with infinite topological degeneracy, in an associated two-dimensional quantum model.