Quark and gluon entanglement in the proton on the light cone at intermediate x
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Entanglement asymmetry and symmetry defects in boundary conformal field theory
A state in a quantum system with a given global symmetry, G, can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G-symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.
Field Theories in Lower Dimensions↗
On de Sitter spacetime and string theory
We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, [Formula: see text]-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.
Astronomy & Astrophysics↗
Explicit entropic proofs of irreversibility theorems for holographic RG flows
We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F -, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic c-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: there, we reprove the monotonicity of flows from AdS D+1 to AdS 3 and prove the novel case of flows from AdS 5 to AdS 4 .
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Generalized entanglement entropies in two-dimensional conformal field theory
We introduce and study generalized Rényi entropies defined through the traces of products of Tr B (| Ψ i $\rangle$$\langle$Ψ j | ) where |Ψ i $\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT). When |Ψ i $\rangle$ = |Ψ j $\rangle$ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The dual of non-extremal area: differential entropy in higher dimensions
The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancelation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in AdS 4 . Our results suggest a candidate c-function for field theories in arbitrary dimensions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Efficient simulation of low-temperature physics in one-dimensional gapless systems
Here, we discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index 0 < q ≤ 1. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as O(cN 0 logβ) where c is the central charge and N is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Entanglement rearrangement in self-consistent nuclear structure calculations
Background: Entanglement plays a central role in a diverse array of increasingly important research areas, including quantum computation, simulation, measurement, sensing, and communication. Extensive suites of investigations have been performed to better understand entanglement in atomic and molecular quantum many-body systems, while the exploration of entanglement in the structure of nuclei and their reactions is presently in its infancy. Purpose: The goal of this work is to begin investigating the entanglement properties of nuclei from first-principles nuclear many-body calculations. We attempt to identify common features and emergent structures of entanglement that could ultimately lead to new and natural many-body schemes. With an eye toward quantum accelerators in future hybrid-supercomputers, criteria for partitioning nuclear many-body calculations into quantum and classical components may provide advantages in future large-scale computations. Along the way we look for explanations of the relative success of phenomenological models such as the nuclear shell model, and for better ways to match to low-energy nuclear effective field theories and lattice QCD calculations to nuclear many-body techniques that are based upon entanglement. Method: We explore the entanglement between single-particle states in 4 He and 6 He. The patterns of entanglement emerging from different single-particle bases are compared, and possible links with the convergence of observables are explored, in particular, ground-state energies. The nuclear wave functions are obtained by performing active-space no-core configuration-interaction calculations using a two-body nucleon-nucleon interaction derived from chiral effective field theory. Entanglement measures within single-particle bases exhibiting different degrees of complexity are determined, in particular, harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational natural (VNAT) bases. Specifically, single-orbital entanglement entropy, two-orbital mutual information, and negativity are studied. Results: The entanglement structures in 4 He and 6 He are found to be more localized within NAT and VNAT bases than within a HO basis for the optimal HO parameters we have worked with. In particular a core-valence structure clearly emerges from the full no-core calculation of 6 He. Here, the two-nucleon mutual information shows that the VNAT basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. Conclusions: Measures of one- and two-nucleon entanglement are found to be useful in analyzing the structure of nuclear wave functions, in particular the efficacy of basis states, and may provide useful metrics toward developing more efficient schemes for ab initio computations of the structure and reactions of nuclei, and quantum many-body systems more generally.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Geometric quantum information structure in quantum fields and their lattice simulation
An upper limit to distillable entanglement between two disconnected regions of massless noninteracting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. Here, we highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Postquantum Quench Growth of Renyi Entropies in Low-Dimensional Continuum Bosonic Systems
The growth of Renyi entropies after the injection of energy into a correlated system provides a window upon the dynamics of its entanglement properties. Here we develop a simulation scheme by which this growth can be determined in Luttinger liquids systems with arbitrary interactions, even those introducing gaps into the liquid. We apply this scheme to an experimentally relevant quench in the sine-Gordon field theory. While for short times we provide analytic expressions for the growth of the second and third Renyi entropy, to access longer times, we combine our scheme with truncated spectrum methods.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
$c$-functions in flows across dimensions
We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d N =4 SYM and compactifications of 6d N = (2, 0) theories.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Mean-field entanglement transitions in random tree tensor networks
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Inverted c-functions in thermal states
We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $\mathcal{N}$ = 4 Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Fixed-point quantum circuits for quantum field theories
Renormalization group ideas and effective operators are introduced to efficiently prepare ground states of massive lattice field theories on digital quantum devices. This is accomplished with a systematic approximation through localized unitaries that removes an exponentially costly barrier in the spatial volume of the quantum simulation. With these methods, classically computed ground states in a spatial volume L, containing a few Compton wavelengths, can be used to determine operators for preparing the ground state toward the thermodynamic limit with a precision improving as e –mL on beyond-classical quantum registers. Here, due to the exponential spatial decay of correlations in massive theories and the double exponential suppression of digitization artifacts in the number of qubits representing the scalar field, the derived fixed-point quantum circuits are expected to be relevant for simulations of quantum field theories throughout the evolution from small-scale near-term quantum devices to large-scale fault-tolerant quantum computers.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Quantum entanglement correlations in double quark PDFs
Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions x 1 and x 2 . A nonperturbative three quark model light-cone wavefunction predicts significant nonclassical correlations associated with the “entanglement negativity” measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher Q 2 scale, the nonclassical correlations manifest in the dPDF for nearly symmetric momentum fractions.
Entanglement in field theory↗
Steps toward quantum simulations of hadronization and energy loss in dense matter
A framework for simulating the real-time dynamics of composite particles in a simple model of dense matter that is amenable to quantum computers is developed. As a demonstration, we perform classical simulations of heavy-hadrons propagating through a dense medium in the Schwinger model. Measurements of the time-dependent energy and charge density are used to identify mechanisms responsible for energy loss and hadron production (hadronization). A study of entanglement dynamics highlights the importance of quantum coherence between the particles that make up the dense medium. Throughout this work, care is taken to isolate, and remove, phenomena that arise solely from a finite lattice spacing. It is found that signatures of entanglement are more sensitive to lattice artifacts than other observables. Toward quantum simulations, we present an efficient method and the corresponding quantum circuits for preparing ground states in the presence of heavy mesons. Finally, these circuits are used to estimate the resources required to simulate in-medium energy loss and hadronization in the Schwinger model using quantum computers.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Complexity for link complement states in Chern-Simons theory
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Including contributions from entanglement islands to the reflected entropy
Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in quantum field theory states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includes additional contributions from such islands. We derive this formula from the gravitational path integral by finding additional saddles that include generalized replica wormholes. We also demonstrate that our covariant formula satisfies all the inequalities required of the reflected entropy. We use this formula in various examples that demonstrate its relevance in illustrating the structure of multipartite entanglement that are invisible to the entropies.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗