<p>Recently, subdimensional particles including fractons have attracted much attention from various areas. Notable features of such matter phases are mobility constraints and subextensive ground-state degeneracies (GSDs). In this paper, we propose a BF-like theory motivated by the Godbillon-Vey invariant, which is a mathematical invariant of the foliated manifold. Our theory hosts subsystem higher-form symmetries which manifestly ensure the mobility constraint and subextensive GSD through the spontaneous symmetry breaking. We also discuss some lattice spin models which realize the same low-energy behaviors as the BF-like theory. Furthermore, we explore dynamical matter theories which are coupled to the BF-like theory.</p>

Japan

Hiromi Ebisu

Masazumi Honda

Taiichi Nakanishi

Soichiro Shimamori

New field theories with foliation structure and subdimensional particles from the Godbillon-Vey invariant

The spontaneous breaking of CP symmetry in 4D SU($\textit{N}$) pure Yang-Mills theory at $\textit{θ}$ = $\textit{π}$ has recently attracted much attention in the context of the higher-form symmetry and the ’t Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $\textit{N}$ = 2 case, which is interesting since it is the case opposite to the large-$\textit{N}$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $\textit{θ}$ term for real $\textit{θ}$, we first obtain results at imaginary $\textit{θ}$, where the sign problem is absent, and make an analytic continuation to real $\textit{θ}$. We use the stout smearing in defining the $\textit{θ}$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $\textit{θ}$ = $\textit{π}$, and provide evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored $\textit{strictly above}$ the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$\textit{N}$ limit.

Italy

Mitsuaki Hirasawa

Akira Matsumoto

Jun Nishimura

Atis Yosprakob

Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\textit{θ}$ = $\textit{π}$ from imaginary $\textit{θ}$ simulations

In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied — multipole symmetry, associated with conservation of multipoles. Based on algebraic relation between dipole and global charges, we introduce a series of (d + 1)-dimensional BF theories with p-form gauge fields, which admit dipole of spatially extended excitations, and study their physical properties. We elucidate that gauge invariant loops have unusual form, containing linear function of the spatial coordinate, which leads to the position dependent braiding statistics and unusual ground state degeneracy dependence on the system size. We also show that the theories exhibit a mixed ’t Hooft anomaly between p-form and (d − p)-form dipole symmetries, which is canceled by an invertible theory defined in one dimensional higher via anomaly inflow mechanism.

Anomaly inflow for dipole symmetry and higher form foliated field theories

We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

Ryusuke Jinno

Spain

Lucas Pinol

Koki Tokeshi

Borel resummation of secular divergences in stochastic inflation

We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called ϕ-theory in d + 1 dimensions and discuss its properties studied in literature for d ≤ 3 such as self-duality, vacuum structure, ’t Hooft anomaly, anomaly inflow and lattice regularization. Next we study a theory called chiral ϕ-theory which is an analogue of a chiral boson with subsystem symmetries. Then we discuss theories including fermions with subsystem symmetries. We first construct a supersymmetric version of the ϕ-theory and dropping its bosonic part leads us to a purely fermionic theory with subsystem symmetries called ψ-theory. We argue that lattice regularization of the ψ-theory generically suffers from an analogue of doubling problem as previously pointed out in the d = 3 case. We propose an analogue of Wilson fermion to avoid the “doubling” problem. We also supersymmetrize the chiral ϕ-theory and dropping the bosonic part again gives us a purely fermionic theory. We finally discuss vacuum structures of the theories with fermions and find that they are infinitely degenerate because of spontaneous breaking of subsystem symmetries.

Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

The charge-q Schwinger model is the (1 + 1)-dimensional quantum electrodynamics (QED) with a charge-q Dirac fermion. It has the ℤ q  1-form symmetry and also enjoys the ℤ q  chiral symmetry in the chiral limit, and there is a mixed ’t Hooft anomaly between those symmetries. We numerically study the charge-q Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the ’t Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.

Etsuko Itou

Yuya Tanizaki

DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly

We designed a protocol for digital quantum computation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on <math><mn>1</mn><mo>+</mo><mn>1</mn></math> dimensional quantum electrodynamics with the <math><mi>θ</mi></math> term known as the Schwinger model and test our protocol for this on an IBM simulator. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in the massless case agrees with the known exact result. In the massive case, we find an agreement with mass perturbation theory in the small-mass regime and deviations in the large-mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation appears a promising tool to explore nonperturbative aspects of gauge theories with real time and topological terms.

United Kingdom

Bipasha Chakraborty

United States

Taku Izubuchi

Yuta Kikuchi

Akio Tomiya

Classically emulated digital quantum simulation of the Schwinger model with a topological term via adiabatic state preparation

Abstract We study some properties of generalized global symmetry for the charge-q Schwinger model in the Hamiltonian formalism, which is the (1 + 1)D quantum electrodynamics with a charge-q Dirac fermion. This model has the -form symmetry, which is a remnant of the electric -form symmetry in the pure Maxwell theory. It is known that, if we put the theory on closed space, then the Hilbert space is decomposed into q distinct sectors, called universes, and some states with higher energy density do not decay to the ground state due to the selection rule of the 1-form symmetry. Even with open boundaries, we can observe the stability of such states by seeing a negative string tension behavior, meaning that opposite charges repel each other. In order to see negative string tensions, the vacuum angle θ has to be large enough and the standard path-integral Monte Carlo method suffers from the sign problem. We develop a method based on the adiabatic state preparation to see this feature with digital quantum simulation and confirm it using a classical simulator of quantum devices. In particular, we measure the local energy density and see how it jumps between the inside and outside of the insertion of the probe charges. We explicitly see that the energy density inside is lower than that outside. This is a clear signature of the negative string tension.

Negative string tension of a higher-charge Schwinger model via digital quantum simulation

We perform digital quantum simulation, using a classical simulator, to study screening and confinement in a gauge theory with a topological term, focusing on (<math><mn>1</mn><mo>+</mo><mn>1</mn></math>)-dimensional quantum electrodynamics (Schwinger model) with a theta term. We compute the ground state energy in the presence of probe charges to estimate the potential between them, via adiabatic state preparation. We compare our simulation results and analytical predictions for a finite volume, finding good agreements. In particular our result in the massive case shows a linear behavior for noninteger charges and a nonlinear behavior for integer charges, consistently with the expected confinement (screening) behavior for noninteger (integer) charges.

Lento Nagano

Takuya Okuda

Classically emulated digital quantum simulation for screening and confinement in the Schwinger model with a topological term

We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.