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Tom Banks

Publications and source records attributed to Tom Banks.

At least 37 records · Page 2Linked to original sources
arXiv2023

Holography for Small Values of the Cosmological Constant

We review recent work on holography for finite area causal diamonds and explore its implications for the description of such diamonds in the Anti-deSitter space Conformal Field Theory correspondence. We argue that the algebra of operators in a finite area diamond is well defined in a UV cutoff tensor network construction, but is not related in any simple way to any infinite von Neumann sub-algebra of the boundary algebra or its cross product. Our argument relies on a novel construction of tensor networks that preserves rotation invariance.

hep-th↗
arXiv2022

Exact Low-Energy Solution for Critical Fermi Surfaces

We derive multidimensional bosonization directly from the electron gas in a low-energy, low momentum regime where $ω\gg \frac{k^2}{k_F}$, such that the dispersion can be linearized. To reach this limit, the Fermi momentum and the number of patches are scaled simultaneously keeping the width of each patch finite. We apply this to obtain an exact low-energy solution of the problem of a Fermi surface coupled to a gapless boson, free of disorder and electron-electron scattering. Contrary to claims in the literature, we show that the bosonized theory exactly reproduces the $ω^{2/3}$ of electrons, previously obtained in large-$N$ theories. We argue that correction to the self-energy due to tangential dispersion are subdominant at sufficiently low energies such that $v_F k\gg \left(\frac{g^4 v_F}{k_F}\right)^{1/3} ω^{2/3}$, where $g$ is the coupling constant.

cond-mat.str-el↗
arXiv2022

Comments on the Entanglement Spectrum of de Sitter Space

We argue that the Schwarzschild-de Sitter black hole entropy formula does not imply that the entanglement spectrum of the vacuum density matrix of de Sitter space is flat. Specifically, we show that the expectation value of a random projection operator of dimension $d\gg 1$, on a Hilbert space of dimension $D\gg d$ and in a density matrix $ρ= e^{-K}$ with strictly positive spectrum, is $\frac{d}{D}\left(1 + o(\frac{1}{\sqrt{d}})\right)$, independent of the spectrum of the density matrix. In addition, for a suitable class of spectra the asymptotic estimates ${\rm Tr} (ρK) \sim {\rm ln}\ D - o(1)$ and $ {\rm Tr} [ρ(K - \langle K\rangle)^2] = a \langle K \rangle$ are compatible for any order one constant $a$. We discuss a simple family of matrix models and projections that can replicate such modular Hamiltonians and the SdS entropy formula.

hep-th↗
arXiv2022

JT Gravity Coupled to Fermions

We argue that two-dimensional dilaton gravity models can all be derived from an analog of Jacobson's covariant version of the first law of thermodynamics. We then specialize to the JT gravity model and couple it to massless fermions. This model is exactly soluble in quantum field theory, and we present a new derivation of that result. The field theory model violates two principles one might want to impose on a quantum theory of gravity describing the near horizon region of an extremal charged black hole in four dimensions: finiteness of the entropy for finite causal diamonds, and the absence of global conservation laws. It preserves an infinite number of conservation laws that one would have expected to be violated, since the fermion state on each side of the $AdS_2$ wormhole is unavoidably thermal. We describe a cutoff version of the model, with extra interactions, which cures these difficulties. Our UV completion of the model depends on the AKK map of non-relativistic fermions in an inverted oscillator potential to Weyl fermions in Minkowski space. We argue that gauging the $Z_2$ symmetry of the oscillator model, using a density matrix with temperature that depends on the oscillator coordinates, and inserting chaotic interactions at (almost) infinite oscillator coordinate, we obtain a model with properties expected of quantum gravity in the near horizon region of an extremal charged black hole in four dimensions.

hep-th↗
arXiv2021

Lattice BF Theory, Dumbbells, and Composite Fermions

We formulate $U(1)$ $bda$ Chern-Simons theory, which is also called BF theory, on a lattice, adapting a method proposed by Kantor and Susskind for the groups $\mathbb{R}$ and $\mathbb{Z}_N$. Our method applies to any finite or infinite abelian group. We study the discrete symmetries and use the model to provide a rigorous treatment of the composite fermion theory of the fractional quantum Hall effect (FQHE), with no ambiguities relating to intersecting Wilson/'t Hooft lines. We derive Jain's fractions, and one can also calculate corrections to the mean field solution within this framework. We also generalize the formalism to higher form gauge models in arbitrary dimension, and suggest a possible non-Abelian extension.

hep-th↗
arXiv2021

Comment on Coleman-DeLuccia Instantons

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

hep-th↗
arXiv2021

Entropy and Black Holes in the Very Early Universe

Model independent arguments following from the Covariant Entropy Principle imply that causal diamonds in the very early universe were entirely filled with a single equilibrated system with finite entropy. A universe where this condition persists forever has no localized excitations. Our own universe appears to be headed toward such a state. Within a few hundred times its current age it will approach a state where our local group of galaxies sit in empty de Sitter space. Eventually, the local group collapse into a black hole, which evaporates. Localized excitations in de Sitter space are low entropy constrained states of the vacuum ensemble. The origin of these constraints must be in the early universe: the apparent horizon must expand after some initial period, in a constrained state that is the origin of all localized excitations in the universe. We argue that in global FRW coordinates, this corresponds to slow roll inflation that ends in a dilute gas of tiny black holes, with mass determined by the inflationary scale. We then review arguments that these black holes can account for the Hot Big Bang, baryogenesis, a distinctive pattern of CMB fluctuations, and possibly primordial black hole dark matter consisting of larger black holes that survive until the matter dominated era. The more complicated question of whether these small black holes can evolve in a way that is consistent with all observational constraints requires computer simulations that have not yet been done.

hep-th↗
arXiv2021

On the Colloidal Phase of the Homogeneous Electron Fluid

We provide semi-rigorous arguments that the Homogeneous Electron Fluid (HEF) has a colloidal phase separating the Wigner Crystal from the high density fluid phase. Near the crossover between crystal and fluid ground state energies, the argument is quite general and valid for practically any quantum transition between a crystal and a more amorphous phase. In this regime, the colloid is a gel and its "Goldstone" modes are flows of irregular fluid droplets separated by crystalline walls. A metal insulator transition occurs when a single bubble of fluid spans the entire system. Beyond this transition the colloid is a sol and its properties depend on the existence of meta-stable finite crystallites with negative surface tension. If these exist, the sol phase has lower energy than the homogeneous fluid. In the two dimensional HEF, Kivelson and Spivak argued that such negative surface tension objects always exist, at least in the form of stripes. We argue that the existence of stripes also implies the existence of finite negative tension elliptical crystallites and the detailed competition between the finite crystallite phase and striped phases is difficult to calculate. We also provide weaker arguments that finite crystallites exist in three dimensions. This provides evidence for our claim that the gapless excitations at non-zero wavenumber, observed in the numerical calculations of\cite{haule}\cite{gapless} are quantum remnants of these crystallites (Bosonic quasi-particles) in the limit of vanishing surface tension. Finally, we suggest a Landau mean field theory for the second order quantum phase transition between the fluid and sol phases.

cond-mat.str-el↗
arXiv2020

Path Integrals for Causal Diamonds and the Covariant Entropy Principle

We study causal diamonds in Minkowski, Schwarzschild, (anti) de Sitter, and Schwarzschild-de Sitter spacetimes using Euclidean methods. The null boundaries of causal diamonds are shown to map to isolated punctures in the Euclidean continuation of the parent manifold. Boundary terms around these punctures decrease the Euclidean action by $A_\diamond/4$, where $A_\diamond$ is the area of the holographic screen around the diamond. We identify these boundary contributions with the maximal entropy of gravitational degrees of freedom associated with the diamond.

hep-th↗
arXiv2020

Primordial Black Holes as Dark Matter

We investigate models in which a spectrum of black holes with Hawking temperature of order the radiation temperature at the beginning of the radiation dominated era can survive long enough to produce a matter dominated era at the observed crossover between matter and radiation in our universe. We find that a sufficiently dense population of such black holes can indeed do so. The stronger observational constraint, that the black holes have lifetimes at least as long as the current age of the universe is harder to assess, because of black hole mergers during the matter dominated era. We then investigate whether the required densities and masses are consistent with the Holographic Space-time (HST) model of inflation. We find that they are, but put mild constraints on the slow roll parameter $ε= - \frac{\dot{H}}{H^2}$ in that model to be small. The bound is no stronger than the observational bound on the model's prediction for tensor fluctuations. The required black hole density, at the reheat temperature, in a model with a single species of black hole, must be viewed as a quantum mechanical accident. In such a model, our universe exists because of a low probability quantum fluctuation.

hep-th↗
arXiv2020

Systematic Resummation of the Large N expansion of Vector Models: Application to the Hubbard model and $2 + 1 $ dimensional QED

We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of equations relating all $k-$point charge correlators. $N$ is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large $N$ diagrams, including all diagrams up to some fixed order, for $k$ point functions with $k \leq K$. Higher point functions are replaced with their leading large $N$ behavior. The simplest truncation gives a closed nonlinear equation for the $2$ point function.

hep-th↗
arXiv2020

Holographic Space-time, Newton`s Law, and the Dynamics of Horizons

We revisit the construction of models of quantum gravity in d dimensional Minkowski space in terms of random tensor models, and correct some mistakes in our previous treatment of the subject. We find a large class of models in which the large impact parameter scattering scales with energy and impact parameter like Newton`s law. The scattering amplitudes in these models describe scattering of jets of particles, and also include amplitudes for the production of highly meta-stable states with all the parametric properties of black holes. These models have emergent energy, momentum and angular conservation laws, despite being based on time dependent Hamiltonians. The scattering amplitudes in which no intermediate black holes are produced have a time-ordered Feynman diagram space-time structure: local interaction vertices connected by propagation of free particles (really Sterman-Weinberg jets of particles). However, there are also amplitudes where jets collide to form large meta-stable objects, with all the scaling properties of black holes: energy, entropy and temperature, as well as the characteristic time scale for the decay of perturbations. We generalize the conjecture of Sekino and Susskind, to claim that all of these models are fast scramblers. The rationale for this claim is that the interactions are invariant under fuzzy subgroups of the group of volume preserving diffeomorphisms, so that they are highly non-local on the holographic screen. We review how this formalism resolves the Firewall Paradox.

hep-th↗
arXiv2020

Holographic Theory of Accelerated Observers, the S-matrix, and the Emergence of Effective Field Theory

We present a theory of accelerated observers in the formalism of holographic space time, and show how to define the analog of the Unruh effect for a one parameter set of accelerated observers in a causal diamond in Minkowski space. The key fact is that the formalism splits the degrees of freedom in a large causal diamond into particles and excitations on the horizon. The latter form a large heat bath for the particles, and different Hamiltonians, describing a one parameter family of accelerated trajectories, have different couplings to the bath. We argue that for a large but finite causal diamond the Hamiltonian describing a geodesic observer has a residual coupling to the bath and that the effect of the bath is finite over the long time interval in the diamond. We find general forms of the Hamiltonian, which guarantee that the horizon degrees of freedom will decouple in the limit of large diamonds, leaving over a unitary evolution operator for particles, with an asymptotically conserved energy. That operator converges to the S-matrix in the infinite diamond limit. The S-matrix thus arises from integrating out the horizon degrees of freedom, in a manner reminiscent of, but distinct from, Matrix Theory. We note that this model for the S-matrix implies that Quantum Gravity, as opposed to quantum field theory, has a natural adiabatic switching off of the interactions. We argue that imposing Lorentz invariance on the S-matrix is natural, and guarantees super-Poincare invariance in the HST formalism. Spatial translation invariance is seen to be the residuum of the consistency conditions of HST.

hep-th↗
arXiv2019

Comments on the CKN Bound

Cohen, Kaplan, and Nelson (CKN) conjectured that the UV and IR cutoffs of effective quantum field theories coupled to gravity are not independent, but are connected by the physics of black holes. We interpret the CKN bound as a scale-dependent depletion of the QFT density of states and discuss various aspects of the bound on small and large scales. For laboratory experiments, we argue that the bound provides small corrections to ordinary quantum field theory, which we estimate to be of order $m_e/M_p$ for $g-2$ of the electron. On large scales, we suggest a modification of the CKN bound due to the presence of cosmological horizons and discuss the connection with entropy bounds.

hep-th↗
arXiv2019

On the Low Density Regime of Homogeneous Electron Gas

We investigate the low density limit of the Homogeneous Electron system, often called the {\it Strictly Correlated} regime. We begin with a systematic presentation of the expansion around infinite $r_S$, based on the first quantized treatments suggested in the existing literature. We show that the expansion is asymptotic in the parameter $r_S^{1/4}$ and that the leading order result contains exponential corrections that are significant even for $r_S \sim 100$. Thus, the systematic expansion is of limited utility. As a byproduct of this analysis, we find that there is no Wigner Crystal (WC) in one spatial dimension. This is an example of the Mermin-Wagner theorem, but was not appreciated in some earlier literature. More modern work has come to conclusions identical to ours. Note that the long range Coulomb potential modifies the dispersion relation of phonons in one dimension, but still leads to the instability of the crystal, due to a very weak infrared divergence. We then propose a new approximation scheme based on renormalization group ideas. We show that the Wegner-Houghton-Wilson-Polchinski exact renormalization group equation reduces, in the low density limit, to a classical equation for scale dependent electron and plasmon fields. In principle, this should allow us to lower the wave number cutoff of the model to a point where Wigner's intuitive argument for dominance of the classical Coulomb forces becomes rigorously correct.

cond-mat.str-el↗
arXiv2019

Instantons, Colloids and Convergence of the 1/N Expansion for the Homogeneous Electron Gas

We investigate non-perturbative corrections to the large $N$ expansion of the homogeneous electron gas. These are associated with instanton solutions to the effective action of the plasmon field. We show that, although the large field behavior of that action dominates the quadratic bare Coulomb term, there are no solutions at large field, and consequently none at large density. We argue that solutions would exist at low density if the large $N$ theory had a Wigner crystal (WC) phase. However, we argue that this is not the case. Together with the implied convergence of the large $N$ expansion, this implies that the homogeneous electron gas with $N$ component spins and a Coulomb interaction scaling like $1/N$ can only have a WC phase below a curve in the plane of $N$ and density, which asymptotes to zero density at infinite $N$. We argue that for systems with a semi-classical expansion for order parameter dynamics, and a first order quantum transition between fluid and crystal phases, there are instantons associated with the decays of meta-stable fluid and crystal phases in the appropriate regions of the phase diagram. We argue that the crystal will decay into one or more colloidal or bubble phases\cite{kivspiv} rather than directly into the fluid. The transition to a translationally invariant phase is likely to be second order. Unfortunately, the HEG does not have a crystal phase at large $N$, where these semi-classical ideas could be examined in detail. We suggest that the evidence for negative dielectric function at intermediate densities for $N = 2$ is an indicator of this second order transition. It is possible that the closed large $N$ equation for the plasmon two point function, derived in\cite{ergheg} might capture at least the qualitative features of the second order transition.

cond-mat.str-el↗
arXiv2019

Emergent entropy production and hydrodynamics in quantum many-body systems

We study dynamics of a locally conserved energy in ergodic, local many-body quantum systems on a lattice with no additional symmetry. The resulting dynamics is well approximated by a coarse grained, classical linear functional diffusion equation for the probability of all spatial configurations of energy. This is equivalent to nonlinear stochastic hydrodynamics, describing the diffusion of energy in physical spacetime. We find the absence of non-hydrodynamic slow degrees of freedom, a nonlinear fluctuation-dissipation theorem, and the emergence of a (weakly interacting) kinetic theory for hydrodynamic modes near thermal equilibrium. The observable part of the microscopic entropy obeys the local second law of thermodynamics, and quantitatively agrees with the phenomenological predictions of hydrodynamics. Our approach naturally generalizes to ergodic systems with additional symmetries, may lead to numerical algorithms to calculate diffusion constants for lattice models, and implies sufficiency conditions for a rigorous derivation of hydrodynamics in quantum systems.

cond-mat.stat-mech↗