Previous work [SciPost Phys. 14, 129 (2023)] has demonstrated that quantum simulation of abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work, we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk, by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their non-invertibility are also presented.
We show that the effective action that results from integrating out massive Kaehler-Dirac fermions propagating on a curved three dimensional space is a topological gravity theory of Chern-Simons type. In the presence of a domain wall, massless, two dimensional Kaehler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are cancelled via anomaly inflow from the bulk gravitational theory. We also study the invariance of the theory under large gauge transformations. The analysis and conclusions generalize straightforwardly…
Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
Graduate School of Arts and Sciences, University of Tokyo（东京大学大学院人文社会系研究科）；C. N. Yang Institute for Theoretical Physics & Department of Physics and Astronomy, State University of New York at Stony Brook（纽约州立大学石溪分校陈省身理论物理研究所及物理与天文学系）
We study 't Hooft anomalies and the related anomaly inflow for subsystem global symmetries. These symmetries and anomalies arise in a number of exotic systems, including models with fracton order such as the X-cube model. As is the case for ordinary global symmetries, anomalies for subsystem symmetries can be canceled by anomaly inflow from a bulk theory in one higher dimension; the corresponding bulk is therefore a non-trivial subsystem symmetry protected topological (SSPT) phase. We demonstrate these phenomena in several examples with continuous and discrete subsystem global symmetries, as w…
We consider (4+1)-dimensional topologically massive tensor gauge theory. This theory is an analog of the (2+1)-dimensional topologically massive Maxwell-Chern-Simons theory. If the space has a boundary, we find that a (3+1)-dimensional gapless theory appears at the boundary. This gapless theory is a chiral version of the (3+1)-dimensional $φ$ theory. This gapless theory is protected by the anomaly inflow mechanism of subsystem symmetry. We also consider the corner of our topologically massive tensor gauge theory, and find that an infinite number of (1+1)-dimensional chiral bosons appear at the…
Perturbative fermion anomalies in spacetime dimension $d$ have a well-known relation to Chern-Simons functions in dimension $D=d+1$. This relationship is manifested in a beautiful way in "anomaly inflow" from the bulk of a system to its boundary. Along with perturbative anomalies, fermions also have global or nonperturbative anomalies, which can be incorporated by using the $η$-invariant of Atiyah, Patodi, and Singer instead of the Chern-Simons function. Here we give a nonperturbative description of anomaly inflow, involving the $η$-invariant. This formula has been expected in the past based o…
We study a phenomenon that electric charges are "teleported" between two spatially separated objects without exchanging charged particles at all. For example, this phenomenon happens between a magnetic monopole and an axion string in four dimensions, two vortices in three dimensions, and two M5-branes in M-theory in which M2-charges are teleported. This is realized by anomaly inflow into these objects in the presence of cubic Chern-Simons terms. In particular, the Witten effect on magnetic monopoles can be understood as a general consequence of anomaly inflow, which implies that some anomalous…
We extend the recently proposed symmetry breaking scenario of QCD$_3$ to the so-called "master" $(2+1)$d bosonization duality, which has bosonic and fermionic matter on both ends. Using anomaly arguments, a phase diagram emerges with several novel regions. We then construct $2+1$ dimensional dualities for flavored quivers using node-by-node dualization. Such dualities are applicable to theories which live on domain walls in QCD$_4$-like theories with dynamical quarks. We also derive dualities for quivers based on orthogonal and symplectic gauge groups. Lastly, we support the conjectured dualit…
The dualities that map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. However, simplifying assumptions such as Lorentz invariance, low dimensionality, or the absence of axial gauge fields, limit their application to a broad class of systems, including topological semimetals. Here we derive several axial field theory dualities in 2+1 and 3+1 dimensions by developing an axial slave-rotor approach capable of accounting for the axial anomaly. Our 2+1-dimensional duality suggests the existence of a dual, cri…
Non-invertible translation from Lieb-Schultz-Mattis anomaly
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) RIKEN（理化学研究所跨学科理论与数学科学项目）
Anomalies are renormalization group invariants that constrain the dynamics of quantum field theories. We show that certain anomalies for discrete global symmetries imply that the underlying theory either spontaneously breaks its generalized global symmetry or is gapless. We identify an obstruction, formulated in terms of the anomaly inflow action, that must vanish if a symmetry preserving gapped phase, i.e. a unitary topological quantum field theory, exits with the given anomaly. Our result is similar to the $2d$ Lieb-Schultz-Mattis theorem but applies more broadly to continuum theories in gen…
