arXiv subjects

Masataka Watanabe

Publications and source records attributed to Masataka Watanabe.

34 records · Page 2Linked to original sources

arXiv2022

Going beyond ER=EPR in the SYK model

We discuss generalizations of the TFD to a density matrix on the doubled Hilbert space. We suggest that a semiclassical wormhole corresponds to a certain class of such density matrices, and specify how they are constructed. Different semi-classical profiles correspond to different non-overlapping density matrices. We show that this language allows for a finer criteria for when the wormhole is semiclassical, which goes beyond entanglement. Our main tool is the SYK model. We focus on the simplest class of such density matrices, in a scaling limit where the ER bridge is captured by chords going from one space to another, encoding correlations in the microscopic Hamiltonian. The length of the wormhole simply encodes the extent these correlations are eroded when flowing from one side to the other.

hep-th↗

arXiv2021

Fermionization of conformal boundary states

We construct the complete set of boundary states of two-dimensional fermionic CFTs using that of the bosonic counterpart. We see that there are two groups of boundary conditions, which contributes to the open-string partition function by characters with integer coefficients, or with $\sqrt{2}$ times integer coefficients. We argue that, using the argument of [JHEP 09 (2020) 018], this $\sqrt{2}$ indicates a single unpaired Majorana zero mode, and that these two groups of boundary conditions are mutually incompatible. We end the paper by mentioning a possible interpretation of the result in terms of the entanglement entropy.

hep-th↗

arXiv2021

Chern-Simons-Matter Theories at Large Baryon Number

We study $SU(2)$ Chern-Simons theories at level $k$ coupled to a scalar on $T^2\times \mathbb{R}$ at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of $k$ on the IR fixed-point of those models. This classical analysis is valid as long as we take the baryon number large. As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the $O(4)$ Wilson-Fisher fixed-point at large-$k$, as expected from general grounds. This paper will be one primitive step towards quantitative analysis of Chern-Simons-matter dualities using the large charge expansion.

hep-th↗

arXiv2021

Quantum Information Theory of the Gravitational Anomaly

We show that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. We make this precise by decomposing it into two observations: First, a two-dimensional CFT admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary we establish a generalization of the Nielsen-Ninomiya theorem to all two-dimensional unitary local QFTs: No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. We also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature. We advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.

hep-th↗

arXiv2020

Transition of Large $R$-Charge Operators on a Conformal Manifold

We study the transition between phases at large $R$-charge on a conformal manifold. These phases are characterized by the behaviour of the lowest operator dimension $Δ(Q_R)$ for fixed and large $R$-charge $Q_R$. We focus, as an example, on the $D=3$, $\mathcal{N}=2$ Wess-Zumino model with cubic superpotential $W=XYZ+\fracτ{6}(X^3+Y^3+Z^3)$, and compute $Δ(Q_R,τ)$ using the $ε$-expansion in three interesting limits. In two of these limits the (leading order) result turns out to be \begin{equation*} Δ(Q_R,τ)= \begin{cases} \left(\text{BPS bound}\right)\left[1+O(ε|τ|^2Q_R)\right], & Q_R\ll \left\{ \frac{1}ε,\, \frac{1}{ε|τ|^2}\right\}\\ \frac{9}{8}\left(\frac{ε|τ|^2}{2+|τ|^2}\right)^{\frac{1}{D-1}}Q_R^{\frac{D}{D-1}} \left[1+O\left(\left(ε|τ|^2Q_R\right)^{-\frac{2}{D-1}}\right)\right], & Q_R\gg \left\{ \frac{1}ε,\, \frac{1}{ε|τ|^2}\right\} \end{cases} \end{equation*} which leads us to the double-scaling parameter, $ε|τ|^2Q_R$, which interpolates between the "near-BPS phase" ($Δ(Q)\sim Q$) and the "superfluid phase" ($Δ(Q)\sim Q^{D/(D-1)}$) at large $R$-charge. This smooth transition, happening near $τ=0$, is a large-$R$-charge manifestation of the existence of a moduli space and an infinite chiral ring at $τ=0$. We also argue that this behavior can be extended to three dimensions with minimal modifications, and so we conclude that $Δ(Q_R,τ)$ experiences a smooth transition around $Q_R\sim 1/|τ|^2$. Additionally, we find a first-order phase transition for $Δ(Q_R,τ)$ as a function of $τ$, as a consequence of the duality of the model. We also comment on the applicability of our result down to small $R$-charge.

hep-th↗

arXiv2020

S-duality and correlation functions at large R-charge

We study the ratio of pairs of adjacent correlators of Coulomb-branch operators in $SU(2)$ $\mathcal{N}=2$ SQCD with four flavors within the framework of the Large Quantum Number Expansion. Capitalizing on the order-by-order S-duality invariance of the large-R-charge expansion we compute ab initio the dependence of the leading large-$\mathcal{J}$ behavior on the marginal coupling $τ$ and we find excellent agreement with numerical estimates from localization.

hep-th↗

arXiv2019

On the CFT Operator Spectrum at Large Global Charge

We calculate the anomalous dimensions of operators with large global charge $J$ in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a $W = Φ^3$ superpotential. Working in a $1/J$ expansion, we find that the large-$J$ sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge $J$ is always a scalar operator whose dimension $Δ_J$ satisfies the sum rule $ J^2 Δ_J - \left( \tfrac{J^2}{2} + \tfrac{J}{4} + \tfrac{3}{16} \right) Δ_{J-1} - \left( \tfrac{J^2}{2} - \tfrac{J}{4} + \tfrac{3}{16} \right) Δ_{J+1} = 0.035147 $ up to corrections that vanish at large $J$. The spectrum of low-lying excited states is also calculable explcitly: For example, the second-lowest primary operator has spin two and dimension $Δ\ll J + \sqrt{3}$. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order $J^{1/2}$. The propagation speeds of the Goldstone waves and heavy fermions are $\frac{1}{\sqrt{2}}$ and $\pm \frac{1}{2}$ times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large $J$.

hep-th↗

arXiv2019

Universal correlation functions in rank 1 SCFTs

Carrying to higher precision the large-$\mathcal{J}$ expansion of Hellerman and Maeda, we calculate to all orders in $1/\mathcal{J}$ the power-law corrections to the two-point functions $\mathcal{Y}_n \equiv |x - y|^{2nΔ_{\mathcal{O}}} \langle {\mathcal{O}}_n(x) \bar{\mathcal{O}}_n(y) \rangle$ for generators $\mathcal{O}$ of Coulomb branch chiral rings in four-dimensional $\mathcal{N} =2$ superconformal field theories. We show these correlators have the universal large-$n$ expansion \[ \log(\mathcal{Y}_n) \simeq \mathcal{J} \mathbf{A} + \mathbf{B} + \log(Γ( \mathcal{J} + α+ 1)) , \] where $\mathcal{J} \equiv 2 n Δ_{\mathcal{O}}$ is the total $R$-charge of $\mathcal{O}_n$, the $\mathbf{A}$ and $\mathbf{B}$ are theory-dependent coefficients, $α$ is the coefficient of the Wess-Zumino term for the Weyl $a$-anomaly, and the $\simeq$ denotes equality up to terms exponentially small in $\mathcal{J}$. Our methods combine the structure of the Coulomb-branch effective field theory (EFT) with the supersymmetric recursion relations. However, our results constrain the power-law corrections to all orders, even for non-Lagrangian theories to which the recursion relations do not apply. For the case of $\mathcal{N} = 2$ SQCD, we also comment on the nature of the exponentially small corrections, which can be calculated to high precision in the double-scaling limit recently discussed by Bourget et al. We show the exponentially small correction is consistent with the interpretation of the EFT breaking down due to the propagation of massive BPS particles over distances of order of the infrared scale $|x - y|$.

hep-th↗

arXiv2019

Accessing Large Global Charge via the $ε$-Expansion

We compute the lowest operator dimension $Δ(J;D)$ at large global charge $J$ in the $O(2)$ Wilson-Fisher model in $D=4-ε$ dimensions, to leading order in both $1/J$ and $ε$. The final result for $Δ(J;D)$ in the (resummed) $ε$-expansion, valid when $J\gg 1/ε\gg 1$, turns out to be \begin{equation*} Δ(J;D)=\left[\frac{2(D-1)}{3(D-2)}\left(\frac{9(D-2)π}{5D}\right)^{\frac{D}{2(D-1)}}\left[\frac{5Γ\left(\frac{D}{2}\right)}{24π^2}\right]^{\frac{1}{D-1}} ε^{\frac{D-2}{2(D-1)}}\right]\times J^{\frac{D}{D-1}}+O\left(J^{\frac{D-2}{D-1}}\right) \end{equation*} where next-to-leading order onwards were not computed here due to technical cumbersomeness, despite there are no fundamental difficulties. We also compare the result at $ε=1$, \begin{equation*} Δ(J)=0.293\times J^{3/2}+\cdots \end{equation*} to the actual data from the Monte-Carlo simulation in three dimensions \cite{Banerjee:2017fcx}, and the discrepancy of the coefficient $0.293$ from the numerics turned out to be $13\%$. Additionally, we also find a crossover of $Δ(J;D)$ from $Δ(J)\propto J^{\frac{D}{D-1}}$ to $Δ(J)\propto J$, at around $J\sim 1/ε$, as one decreases $J$ while fixing $ε$ (or vice versa), reflecting the fact that there are no interacting fixed-point at $ε=0$. Based on this behaviour, we propose an interesting double-scaling limit which fixes $λ\equiv Jε$, suitable for probing the region of the crossover. I will give $Δ(J;D)$ to next-to-leading order in perturbation theory, either in $1/λ$ or in $λ$, valid when $λ\gg 1$ and $λ\ll 1$, respectively.

hep-th↗

arXiv2018

Page Curves for General Interacting Systems

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [Nature Communications 9, 1635 (2018)], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, $S_2(\ell)=-\ln K(β)+\ell\ln a(β)-\ln\left(1+a(β)^{-L+2\ell}\right)$, where $L$ is the total volume of the system and $a$ and $K$ are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.

cond-mat.stat-mech↗

arXiv2018

Universality in volume law entanglement of pure quantum states

A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases, however, quantum correlations break the correspondence and cause a correction to this simple volume-law. To elucidate the size dependence of the entanglement entropy is of essential importance in linking quantum physics with thermodynamics, and in addressing recent experiments in ultra-cold atoms. Here we derive an analytic formula of the entanglement entropy for a class of pure states called cTPQ states representing thermal equilibrium. We further find that our formula applies universally to any sufficiently scrambled pure states representing thermal equilibrium, i.e., general energy eigenstates of non-integrable models and states after quantum quenches. Our universal formula can be exploited as a diagnostic of chaotic systems; we can distinguish integrable models from chaotic ones and detect many-body localization with high accuracy.

cond-mat.stat-mech↗

arXiv2018

Observables in Inhomogeneous Ground States at Large Global Charge

As a sequel to previous work, we extend the study of the ground state configuration of the $D=3$, Wilson-Fisher conformal $O(4)$ model. In this work, we prove that for generic ratios of two charge densities, $ρ_1/ρ_2$, the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for $ρ_1/ρ_2\ll 1$. We also compute, at fixed set of charges, $ρ_1,\, ρ_2$, the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale $(ρ_1+ρ_2)^{3/2}$, as dictated by dimensional analysis and similarly to the case of the $O(2)$ model. Unlike the case of the $O(2)$ model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

hep-th↗

arXiv2017

Operator Dimensions from Moduli

We consider the operator spectrum of a three-dimensional ${\cal N} = 2$ superconformal field theory with moduli spaces of one complex dimension, such as the fixed point theory with three chiral superfields $X,Y,Z$ and a superpotential $W = XYZ$. By using the existence of an effective theory on each branch of moduli space, we calculate the anomalous dimensions of certain low-lying operators carrying large $R$-charge $J$. While the lowest primary operator is a BPS scalar primary, the second-lowest scalar primary is in a semi-short representation, with dimension exactly $J+1$, a fact that cannot be seen directly from the $XYZ$ Lagrangian. The third-lowest scalar primary lies in a long multiplet with dimension $J+2 - c_{-3} \, J^{-3} + O(J^{-4})$, where $c_{-3}$ is an unknown positive coefficient. The coefficient $c_{-3}$ is proportional to the leading superconformal interaction term in the effective theory on moduli space. The positivity of $c_{-3}$ does not follow from supersymmetry, but rather from unitarity of moduli scattering and the absence of superluminal signal propagation in the effective dynamics of the complex modulus. We also prove a general lemma, that scalar semi-short representations form a module over the chiral ring in a natural way, by ordinary multiplication of local operators. Combined with the existence of scalar semi-short states at large $J$, this proves the existence of scalar semi-short states at all values of $J$. Thus the combination of ${\cal N}=2$ superconformal symmetry with the large-$J$ expansion is more powerful than the sum of its parts.

hep-th↗

arXiv2017

A Note on Inhomogeneous Ground States at Large Global Charge

In this note we search for the ground state, in infinite volume, of the $D=3$ Wilson-Fisher conformal $O(4)$ model, at nonzero values of the two independent charge densities $ρ_{1,2}$. Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios $ρ_1 / ρ_2$. This result confirms, within the context of a well-defined effective theory, a recent no-go result of Alvarez-Gaume' et al. We also show that any spatially periodic ground state solutions have an energetic preference towards longer periods, within some range of $ρ_1 / ρ_2$ containing a neighborhood of zero. This suggests that the scale of variation of the ground state solution in finite volume will be the infrared scale, and that the use of the effective theory at large charge in finite volume is self-consistent.

hep-th↗

arXiv2015

Electronic structure of helicoidal graphene: massless Dirac particles on a curved surface with a screw symmetry

Massless Dirac particles on the helicoid are theoretically investigated. With its possible application being helical graphene, we explore how the peculiarities of Dirac particles appear on the curved, screw-symmetric surface. The zweibein is used to derive the massless Dirac equation on the helicoid, as well as general curved surfaces. Bound states of massless Dirac electrons are shown to be absent on the helicoid, and then the scattering probabilities and the phase shifts on the surface are obtained from numerically calculated wave functions. We find the local density of states and the phase shifts idiosyncratic especially around the axis of the helicoid. Bound states of massive Dirac electrons on the surface are also shown to be absent as an extension of the above result on massless Dirac electrons.

cond-mat.mes-hall↗

arXiv2005

Short-term Synaptic Depression Improves Error-correcting Ability in Cortical Circuits

Synaptic connections are known to change dynamically. High-frequency presynaptic inputs induce decrease of synaptic weights. This process is known as short-term synaptic depression. The synaptic depression controls a gain for presynaptic inputs. However, it remains a controversial issue what are functional roles of this gain control. We propose a new hypothesis that one of the functional roles is to enlarge basins of attraction. To verify this hypothesis, we employ a binary discrete-time associative memory model which consists of excitatory and inhibitory neurons. It is known that the excitatory-inhibitory balance controls an overall activity of the network. The synaptic depression might incorporate an activity control mechanism. Using a mean-field theory and computer simulations, we find that the basins of attraction are enlarged whereas the storage capacity does not change. Furthermore, the excitatory-inhibitory balance and the synaptic depression work cooperatively. This result suggests that the synaptic depression works to improve an error-correcting ability in cortical circuits.

cond-mat.dis-nn↗