More Like this

1. Treelike structure of symmetry topological field theories and multisector QFTs

   https://doi.org/10.1103/PhysRevD.109.106013  

   Baume, Florent; Heckman, Jonathan J; Hübner, Max; Torres, Ethan; Turner, Andrew P; Yu, Xingyang (May 2024, Physical Review D)

   The global symmetries of a $D$-dimensional quantum field theory (QFT) can, in many cases, be captured in terms of a ( $D+1$)-dimensional symmetry topological field theory (SymTFT). In this work we construct a ( $D+1$)-dimensional theory which governs the symmetries of QFTs with multiple sectors which have connected correlators that admit a decoupling limit. The associated symmetry field theory decomposes into a SymTree, namely a treelike structure of SymTFTs fused along possibly nontopological junctions. In string-realized multisector QFTs, these junctions are smoothed out in the extradimensional geometry, as we demonstrate in examples. We further use this perspective to study the fate of higher-form symmetries in the context of holographic large $M$averaging where the topological sectors of different large $M$replicas become dressed by additional extended operators associated with the SymTree. Published by the American Physical Society2024 

   more » « less
2. Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications

   https://doi.org/10.1103/PRXQuantum.5.040330  

   Moudgalya, Sanjay; Motrunich, Olexei I (November 2024, PRX Quantum)

   Symmetry algebras of quantum many-body systems with locality can be understood using commutant algebras, which are defined as algebras of operators that commute with a given set of local operators. In this work, we show that these symmetry algebras can be expressed as frustration-free ground states of a local superoperator, which we refer to as a “super-Hamiltonian.” We demonstrate this for conventional symmetries such as ${\mathbb{Z}}_2$, $U\left(1\right)$, and $SU\left(2\right)$, where the symmetry algebras map to various kinds of ferromagnetic ground states, as well as for unconventional ones that lead to weak ergodicity-breaking phenomena of Hilbert-space fragmentation (HSF) and quantum many-body scars. In addition, we show that the low-energy excitations of this super-Hamiltonian can be understood as approximate symmetries, which in turn are related to slowly relaxing hydrodynamic modes in symmetric systems. This connection is made precise by relating the super-Hamiltonian to the superoperator that governs the operator relaxation in noisy symmetric Brownian circuits and this physical interpretation also provides a novel interpretation for Mazur bounds for autocorrelation functions. We find examples of gapped (gapless) super-Hamiltonians indicating the absence (presence) of slow modes, which happens in the presence of discrete (continuous) symmetries. In the gapless cases, we recover hydrodynamic modes such as diffusion, tracer diffusion, and asymptotic scars in the presence of $U\left(1\right)$symmetry, HSF, and a tower of quantum scars, respectively. In all, this demonstrates the power of the commutant-algebra framework in obtaining a comprehensive understanding of exact symmetries and associated approximate symmetries and hydrodynamic modes, and their dynamical consequences in systems with locality. Published by the American Physical Society2024 

   more » « less
3. Noninvertible Symmetry-Protected Topological Order in a Group-Based Cluster State

   https://doi.org/10.1103/PhysRevX.15.011058  

   Fechisin, Christopher; Tantivasadakarn, Nathanan; Albert, Victor V (March 2025, Physical Review X)

   Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a $G\times \mathrm{Rep}\left(G\right)$-symmetric state: the $G$-cluster state introduced by Brell []. We show that this state lies in a symmetry-protected topological (SPT) phase protected by $G\times \mathrm{Rep}\left(G\right)$symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely, protected edge modes, string order parameters, and topological response. We discuss how $G$-cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where $G$is a semidirect product of Abelian groups. Published by the American Physical Society2025 

   more » « less
4. Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

   https://doi.org/10.1103/PRXQuantum.6.010341  

   Liu, Zhenning; Devulapalli, Dhruv; Hangleiter, Dominik; Liu, Yi-Kai; Kollár, Alicia J; Gorshkov, Alexey V; Childs, Andrew M (March 2025, PRX Quantum)

   Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on verification of an analog quantum simulation, in which the verifier need only run an $O\left({\lambda }^2\right)$-time classical computation, and the prover need only prepare $O\left(1\right)$samples of a history state and perform $O\left({\lambda }^2\right)$single-qubit measurements, for a security parameter $\lambda$. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations. Published by the American Physical Society2025 

   more » « less
5. Quantized Axial Charge of Staggered Fermions and the Chiral Anomaly

   https://doi.org/10.1103/PhysRevLett.134.021601  

   Chatterjee, Arkya; Pace, Salvatore D; Shao, Shu-Heng (January 2025, Physical Review Letters)

   In the $1+1\mathrm{D}$ultralocal lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac fermion with a perturbative anomaly. Each of the two lattice charges generates an ordinary U(1) global symmetry that acts locally on operators and can be gauged individually. Interestingly, they do not commute on a finite lattice and generate the Onsager algebra, but their commutator goes to zero in the continuum limit. The chiral anomaly is matched by this non-Abelian algebra, which is consistent with the Nielsen-Ninomiya theorem. We further prove that the presence of these two conserved lattice charges forces the low-energy phase to be gapless, reminiscent of the consequence from perturbative anomalies of continuous global symmetries in continuum field theory. Upon bosonization, these two charges lead to two exact U(1) symmetries in the XX model that flow to the momentum and winding symmetries in the free boson conformal field theory. Published by the American Physical Society2025 

   more » « less