# Sine-square deformation and Möbius quantization of 2D conformal field theory

@article{Okunishi2016SinesquareDA, title={Sine-square deformation and M{\"o}bius quantization of 2D conformal field theory}, author={Kouichi Okunishi}, journal={Progress of Theoretical and Experimental Physics}, year={2016}, volume={2016} }

Motivated by sine-square deformation (SSD) for quantum critical systems in 1+1-dimension, we discuss a Mobius quantization approach to the two-dimensional conformal field theory (CFT), which bridges the conventional radial quantization and the dipolar quantization recently proposed by Ishibashi and Tada. We then find that the continuous Virasoro algebra of the dipolar quantization can be interpreted as a continuum limit of the Virasoro algebra for scaled generators in the SSD limit of the…

## 20 Citations

Zero-energy states in conformal field theory with sine-square deformation

- Physics, Mathematics
- 2017

We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of finite norm for the Hamiltonian of a unitary…

Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to nonuniform conformal field theory

- PhysicsPhysical Review B
- 2018

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the non-equilibrium quantum dynamics of a conformal field theory (CFT) with SSD,…

Conformal quantum mechanics and sine-square deformation

- PhysicsProgress of Theoretical and Experimental Physics
- 2018

We revisit conformal quantum mechanics (CQM) from the perspective of sine-square deformation (SSD) and the entanglement Hamiltonian. The operators that correspond to SSD and the entanglement…

Time development of conformal field theories associated with L 1 and L −1 operators

- Physics, Mathematics
- 2020

In this study, we examined consequences of unconventional time development of two-dimensional conformal field theory induced by the $L_{1}$ and $L_{-1}$ operators, employing the formalism previously…

Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases

- Physics, Mathematics
- 2021

In this sequel (to [Phys. Rev. Res. 3, 023044(2021)], arXiv:2006.10072), we study randomly driven (1+1) dimensional conformal field theories (CFTs), a family of quantum many-body systems with soluble…

Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory

- Physics
- 2019

We study the energy and entanglement dynamics of $(1+1)$D conformal field theories (CFTs) under a Floquet drive with the sine-square deformed (SSD) Hamiltonian. Previous work has shown this model…

Closed string symmetries in open string field theory: tachyon vacuum as sine-square deformation

- PhysicsProgress of Theoretical and Experimental Physics
- 2018

We revisit the identity-based solutions for tachyon condensation in open bosonic string field theory (SFT) from the viewpoint of the sine-square deformation (SSD). The string Hamiltonian derived from…

Holographic duals of inhomogeneous systems: the rainbow chain and the sine-square deformation model

- Physics
- 2018

A holographic dual description of inhomogeneous systems is discussed. Notably, finite temperature results for the entanglement entropy in both the rainbow chain and the SSD model are obtained…

Magnetic susceptibility of quantum spin systems calculated by sine square deformation: One-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets

- PhysicsPhysical Review B
- 2018

We develop a simple and unbiased numerical method to obtain the uniform susceptibility of quantum many-body systems. When a Hamiltonian is spatially deformed by multiplying it with a sine-square…

Emergent black hole dynamics in critical Floquet systems

- Physics
- 2020

While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. We study such an exceptional class in periodically driven…

## References

SHOWING 1-10 OF 18 REFERENCES

Sine-square deformation and supersymmetric quantum mechanics

- Physics
- 2015

We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space. On the basis of supersymmetric quantum mechanics, we prove the correspondence between the…

Sine-Square Deformation and its Relevance to String Theory

- Physics
- 2014

Sine-square deformation, a recently found modulation of the coupling strength in certain statistical models, is discussed in the context of two-dimensional conformal field theories, with particular…

Sine-square deformation of solvable spin chains and conformal field theories

- Physics
- 2012

We study solvable spin chains, one-dimensional massless Dirac fermions and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the…

Infinite circumference limit of conformal field theory

- Physics
- 2015

We argue that an infinite circumference limit can be obtained in 2-dimensional conformal field theory by adopting $L_0-(L_1+L_{-1})/2$ as a Hamiltonian instead of $L_0$. The theory obtained has a…

Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory - Nucl. Phys. B241, 333 (1984)

- Physics
- 1984

Sine-square deformation of free fermion systems in one and higher dimensions

- Physics
- 2011

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[\pi(x-1/2)/L], where x…

Connecting distant ends of one-dimensional critical systems by a sine-square deformation

- Physics
- 2011

We study the one-dimensional quantum critical spin systems with the sine-square deformation, in which the energy scale in the Hamiltonian at the position $x$ is modified by the function $f_x =…

Spherical Deformation for One-Dimensional Quantum Systems

- Physics
- 2008

System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards…

Global conformal invariance in quantum field theory

- Mathematics
- 1975

AbstractSuppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group⋍SOe(5,1). We show that its Hilbert space of…