A new class of quantum entanglement transitions separating phases with different entropy scaling has been observed in recent numerical studies. Despite the efforts, an analytical understanding such remained elusive. Here, authors propose a theory for area-law to volume-law transition many-body systems that undergo both random unitary evolutions and projective measurements. Using replica method, map analytically this ordering classical statistical mechanics model. They derive general...

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical for randomly interaction fermions in dot. This paper studies the properties of many-body spectrum SYK and finds periodicity spectral term number fermion modes In particular, level statistics are investigated. It found that spacing follows Wigner-Dyson statistics, consistent with thermalizing nature model. Interestingly, goes through those different random matrix ensembles periodically. can be explained by viewing as an effective...

We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example such an "entanglement transition" is provided by the many-body localization transition in disordered systems, as it separates highly entangled thermal at weak disorder from localized low strong disorder. In spirit random matrix theory, we describe simple model for where physical system lives "holographic" boundary bulk tensor network. Using replica trick approach, map...

We develop a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, fermiology consists of well nested pockets derived opposite valleys, leading enhanced valley fluctuation, which turn can mediate superconductivity. This scenario studied within random phase approximation. find inter-valley electron pairing with either chiral ($d+i d$ mixed $p-i p$) or helical form factor dominant...

Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of exceeds threshold value. Below this threshold, steady state with sub-thermal volume law entanglement emerges, which is resistant disentangling action measurements, suggesting connection error-correcting codes. Here we quantify these notions by identifying universal, subleading logarithmic contribution entropy: $S^{(2)}(A)=\kappa...

We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where ensemble is invariant under local-basis transformations. In this case, reconstruction map for depends only on average entanglement feature snapshots. provide an unbiased estimator state linear combination reduced snapshots in all subsystems, coefficients are solely determined by feature. also bound number experimental...

A Kitaev-Heisenberg-${J}_{2}$-${J}_{3}$ model is proposed to describe the Mott-insulating layered iridates ${A}_{2}$IrO${}_{3}$ ($A=\text{Na}$, Li). The a combination of Kitaev honeycomb and Heisenberg with all three nearest-neighbor couplings ${J}_{1}$, ${J}_{2}$, ${J}_{3}$. rich phase diagram obtained at classical level, including experimentally suggested zigzag ordered phase; as well stripy phase, which extends from Kitaev-Heisenberg limit ${J}_{1}$-${J}_{2}$-${J}_{3}$ one. Combining...

We study the effects of doping a Mott insulator on honeycomb lattice where spins interact via direction dependent Kitaev couplings J_K, and weak antiferromagnetic Heisenberg J. This model is known to have spin liquid ground state may potentially be realized in correlated insulators with strong orbit coupling. The effect hole studied within t-J-J_K model, treated using SU(2) slave boson formulation, which correctly captures parent liquid. find superconductor states triplet pairing that...

Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, construct Z_N rotor model that realizes self-dual Abelian gauge theory. We find lattice dislocation defects in the produce degeneracy. Even though dislocations are not excitations, they resemble anyons with quantum dimension sqrt(N). Exchanging can produces projective phases. The dislocations, be viewed generalization Majorana zero modes.

We investigate the generic features of low energy dynamical spin structure factor Kitaev honeycomb quantum liquid perturbed away from its exact soluble limit by symmetry-allowed exchange couplings. find that gap persists in Kitaev-Heisenberg model, but generally vanishes provided more interactions exist. formulate expansion operator terms fractionalized Majorana fermion operators according to symmetry enriched topological order liquid, described projective group. The displays power-law...

We study the classification for a large class of interacting fermionic and bosonic symmetry-protected topological (SPT) states, focusing on cases where interaction reduces free-fermion SPT states. define state as whether it is separated from trivial through bulk phase transition, which general definition applicable to states with or without spatial symmetries. show that in all dimensions short-range interactions can reduce we demonstrate these results by making connection between first our...

Recent theoretical research has focused on exciting new types of phase transitions that do not appear to fit within standard paradigms. In so-called $d\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}f\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}d$ quantum transitions, the conventional quasiparticle used in mathematical descriptions must be replaced by fractionalized...

It is well-known that a stable algebraic spin liquid state (or equivalently an Bose (ABL) state) with emergent gapless photon excitations can exist in quantum ice systems, or dimer model on bipartite $3d$ lattice. This phase against any weak perturbation without assuming symmetry. Further works concluded certain lattice models give rise to more exotic phases graviton-like excitations. In this paper we will show how these states be generalized even types of and then argue new are...

The recent experimental discovery of spin-valley symmetry breaking phases and superconductivity in rhombohedral trilayer graphene has generated much excitement. This research attempts to provide theoretical understanding these phases. A prominent feature the system is existence van Hove singularities electronic band structure. Under interactions, states exhibit a high tendency toward intervalley coherence (IVC) ordering. Upon doping, IVC order can melt, low-lying fluctuations mediate with...

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after spontaneous symmetry breaking, bosonic field that couples fermion term condenses, which grants gap fermionic excitation. In last few years, it was gradually understood there new of generation without involving any breaking within an anomaly-free group, also applicable chiral with symmetries. This generally referred as symmetric (SMG). It realized SMG has deep connections...

Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of quantum state with few measurements. Two classical protocols have been extensively studied in the literature: single-qubit (local) Pauli measurement, which well suited local operators but inefficient large operators; and global Clifford efficient low-rank infeasible on near-term devices due to extensive gate overhead. In this work, we demonstrate scalable approach generic measurements...

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 term or concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address this Letter whether SMG corresponds to true unitary conformal field...

The recent discovery of high-temperature superconductivity in La_{3}Ni_{2}O_{7} offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that electrons d_{z^{2}} orbitals nearly form local moments, we examine effect Hubbard interaction U on binding strength Cooper pairs based single-orbital bilayer model intralayer hopping t_{∥} and interlayer superexchange J_{⊥}. By extensive density matrix renormalization group calculations, observe...

Extracting information efficiently from quantum systems is crucial for processing. Classical shadows enable predicting many properties of arbitrary states using few measurements. While random single-qubit measurements are experimentally friendly and suitable learning low-weight Pauli observables, they perform poorly nonlocal observables. Introducing a shallow circuit before improves sample efficiency high-weight observables low-rank properties. However, in practice, these circuits can be...

Inspired by recent developments in constructing novel Dirac liquid boundary states of a three-dimensional (3D) topological insulator, we propose one possible two-dimensional state 3D bosonic symmetry protected with $U{(1)}_{e}\ensuremath{\rtimes}{Z}_{2}^{T}\ifmmode\times\else\texttimes\fi{}U{(1)}_{s}$ symmetry. This theory is described $(2+1)$-dimensional quantum electrodynamics $({\mathrm{QED}}_{3})$ two flavors fermions $({N}_{f}=2)$ coupled noncompact U(1) gauge field,...

Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel phase transitions. The first is transition between the weakly interacting gapless Dirac fermion and strongly fully gapped symmetric trivial phase, which cannot be described by standard Gross-Neveu model. second critical point spin Hall insulator with ${S}^{z}$ conservation previously mentioned phase. At latter single-particle excitations remain gapped,...

Machine learning is a fast developing area that finds applications in all disciplines of science. Here, the authors demonstrate machine (in particular deep learning) technique can be applied to understand emergence spatial geometry from features quantum many-body entanglement, an idea was proposed recent study holography duality gravity. This work first successfully ``geometry emerging learning''.

We study a possible deconfined quantum phase transition in realistic model of two-dimensional Shastry-Sutherland magnet, using both numerical and field theoretic techniques. Using the infinite density matrix renormalization group (iDMRG) method, we verify existence an intermediate plaquette valence bond solid (pVBS) order, with two fold degeneracy, between dimer N\'eel ordered phases. argue that pVBS orders may be described by critical point (DQCP) emergent O(4) symmetry. By analyzing...

We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of real-space for many-body localized (MBL) system without truncating Hilbert space. Starting from disordered Hamiltonian in full MBL phase, SBRG flows to fixed-point Hamiltonian, and generates local conserved quantities matrix product state representations all eigenstates. The method is applicable both spin fermion models with arbitrary interaction strength on any lattice dimensions, long are phase. In...

Proving an equivalence between two theories---one that describes a transition kinds of insulating states and another models changes spin states---would offer step toward unified theoretical understanding different condensed-matter systems. New computer simulations provide evidence for this duality by showing the critical points these theories have identical properties.