Symmetry-protected topological phases---quantum states typically defined by some exact symmetry---are also well for average symmetries, where disorder locally breaks the symmetry but restores it on average.

Symmetry in mixed quantum states can manifest two distinct forms: , where each individual pure state the ensemble is symmetric with same charge, and which applies only to entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) strong broken weak one. While SSB measured by long-ranged two-point correlation function, strong-to-weak (SWSSB) . We prove that SWSSB universal property mixed-state phases, sense phenomenon robust against low-depth local channels. also...

It has been proposed that the deconfined criticality in $(2+1)d$---the quantum phase transition between a N\'eel antiferromagnet and valence-bond solid (VBS)---may actually be pseudocritical, sense it is weakly first-order with generically long correlation length. The underlying field theory of would slightly complex (nonunitary) fixed point as result points annihilation. This proposal was motivated by existing numerical results from large scale Monte Carlo simulations well conformal...

The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen pure states, can exhibit average symmetries—symmetries that act on component while leaving the ensemble invariant. this work, we systematically characterize symmetry-protected topological (SPT) phases short-range entangled (SRE) spin systems—protected by both exact symmetries—by studying their Choi doubled Hilbert space, where familiar notions tools...

We study the edge physics of deconfined quantum phase transition (DQCP) between a spontaneous spin Hall (QSH) insulator and spin-singlet superconductor (SC). Although bulk this is in same universality class as paradigmatic Neel to valence-bond-solid transition, boundary has richer structure due proximity state. use parton trick write down an effective field theory for QSH-SC presence boundary. calculate various properties N\to\infty <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"...

Global symmetries greatly enrich the landscape of topological quantum phases, playing an essential role from insulators to fractional Hall effect. Topological phases in mixed states, originating decoherence open systems or disorders imperfect crystalline solids, have recently garnered significant interest. Unlike pure states can exhibit average -- that keep total ensemble invariant but not on each individual state. In this work, we present a systematic classification and characterization...

The interplay of symmetry and topology in quantum many-body mixed states has recently garnered significant interest. In a phenomenon not seen pure states, can exhibit average symmetries -- that act on component while leaving the ensemble invariant. this work, we systematically characterize protected topological (SPT) phases short-range entangled (SRE) spin systems by both exact studying their Choi doubled Hilbert space, where familiar notions tools for SRE SPT apply. This advantage space...

We investigate quantum cellular automata (QCA) on one-dimensional spin systems defined over a subalgebra of the full local operator algebra - symmetric under finite Abelian group symmetry $G$. For where each site carries regular representation $G$, we establish complete classification such QCAs based two topological invariants: (1) surjective homomorphism from to anyon permutation symmetries in $(2+1)d$ $G$ gauge theory; and (2) generalization Gross-Nesme-Vogts-Werner (GNVW) index that...

The Fermi liquid has an emergent low-energy symmetry that corresponds to charge conservation at each momentum on the Ferm surface. Recently Else, Thorngren and Senthil (ETS) argued had a specific t'Hooft anomaly. We give simple derivation of ETS anomaly using chiral Weyl fermions.

Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely QCD$_3$-Chern-Simons phase transitions insulators. These are described Dirac fermions interacting with Chern-Simons gauge fields ($U(N)$, $SU(N)$, $USp(N)$, etc.). Utilizing level-rank duality theory and parton constructions, discuss two types QCD$_3$ transitions. The first type happens between...

We employ an $n$-replica Keldysh field theory to investigate the effects of measurements and decoherence on long distance behaviors quantum critical states. classify different based their timescales symmetry properties, demonstrate that they can be described by theories with distinct physical replica symmetries. Low energy effective for various scenarios are then derived using fundamental consistency conditions formalism. apply this framework study Ising model in both one two spatial...

Symmetry-protected topological (SPT) phases are many-body quantum states that topologically nontrivial as long the relevant symmetries unbroken. In this work we show SPT also well defined for average symmetries, where quenched disorders locally break but restore upon disorder averaging. An example would be crystalline with imperfect lattices. Specifically, define notion of disordered ensembles states. We then classify and characterize a large class using decorated domain wall approach, in...

Symmetry in mixed quantum states can manifest two distinct forms: strong symmetry, where each individual pure state the ensemble is symmetric with same charge, and weak which applies only to entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) broken one. While SSB measured by long-ranged two-point correlation function $\mathrm{Tr}(O_xO^{\dagger}_y\rho)$, strong-to-weak (SW-SSB) fidelity $F(\rho, O_xO^{\dagger}_y\rho O_yO^{\dagger}_x)$, dubbed correlator....

We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ rotation and lattice translation symmetries presence of interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two types Hamiltonians are considered: Type I comprises long-range spin-spin couplings, while II features couplings between symmetric local operators. For spin-$\frac{1}{2}$ systems, it is shown that cannot have a unique ground state nonzero excitation gap when interaction decays...