scholarly journals Conformal properties of hyperinvariant tensor networks

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Matthew Steinberg ◽  
Javier Prior
Keyword(s):  
Spin Chain ◽  
Randomized Trials ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Tensor Decompositions ◽  
Conformal Field ◽  
New Class ◽  
Tensor Networks ◽  
Tensor Network ◽  
Original Construction

AbstractHyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of tensor network shows much potential for simulating conformal field theories arising from hyperbolic bulk manifolds with quasiperiodic boundaries, many issues are unresolved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some quasiperiodic critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, implying that the multitensor constraints are neither unique, nor difficult to find, and that a generalization of the analytical tensor forms used up until now may exist. Lastly, we perform randomized trials using a descending superoperator with several of the investigated tensor decompositions, and find that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra of several minimial model CFTs.

scholarly journals Conformal Properties of Hyperinvariant Tensor Networks

2021 ◽  
Author(s):  
Matthew Steinberg ◽  
Javier Prior
Keyword(s):  
Spin Chain ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Tensor Decompositions ◽  
Numerical Evidence ◽  
Conformal Field ◽  
New Class ◽  
Tensor Networks ◽  
Original Construction

Abstract Hyperinvariant tensor networks (hyMERA) were introduced as a way to combine the successes of perfect tensor networks (HaPPY) and the multiscale entanglement renormalization ansatz (MERA) in simulations of the AdS/CFT correspondence. Although this new class of network shows much potential for simulating conformal field theories on hyperbolic bulk manifolds with quasiperiodic boundaries, many issues must still be solved. In this manuscript we analyze the challenges related to optimizing tensors in a hyMERA with respect to some critical spin chain, and compare with standard approaches in MERA. Additionally, we show two new sets of tensor decompositions which exhibit different properties from the original construction, and imply that the multitensor constraints are more general than previously suggested. Lastly, we provide numerical evidence that the constraints imposed on the spectra of local descending superoperators in hyMERA are compatible with the operator spectra for many minimial model CFTs.

scholarly journals Building tensor networks for holographic states

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Pawel Caputa ◽  
Jorrit Kruthoff ◽  
Onkar Parrikar
Keyword(s):  
Path Integral ◽  
Upper Bound ◽  
Field Theories ◽  
Effective Theory ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Tensor Networks ◽  
Tensor Network ◽  
Minimal Area

Abstract We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry. The effective theory in question is the CFT flowed under a $$ T\overline{T} $$ T T ¯ deformation, which “folds” the boundary CFT towards the bulk time-reflection symmetric slice. We propose that these novel Euclidean path integral states in the CFT can be interpreted as continuous tensor network (CTN) states. We argue that these CTN states satisfy a Ryu-Takayanagi-like minimal area upper bound on the entanglement entropies of boundary intervals, with the coefficient being equal to $$ \frac{1}{4{G}_N} $$ 1 4 G N ; the CTN corresponding to the bulk time-reflection symmetric slice saturates this bound. We also argue that the original state of the CFT can be written as a superposition of such CTN states, with the corresponding wavefunction being the bulk Hartle-Hawking wavefunction.

scholarly journals Defects and perturbation

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm
Keyword(s):  
Entanglement Entropy ◽  
Topological Defects ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field

Abstract We investigate perturbatively tractable deformations of topological defects in two-dimensional conformal field theories. We perturbatively compute the change in the g-factor, the reflectivity, and the entanglement entropy of the conformal defect at the end of these short RG flows. We also give instances of such flows in the diagonal Virasoro and Super-Virasoro Minimal Models.

scholarly journals Entanglement and complexity of purification in ( 1+1 )-dimensional free conformal field theories

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Hugo A. Camargo ◽  
Lucas Hackl ◽  
Michal P. Heller ◽  
Alexander Jahn ◽  
Tadashi Takayanagi ◽  
...  
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

scholarly journals NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

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