Solvable Theory Research Articles

Quantum statistical mechanics of the SYK model, charged black holes, and strange metals

The Sachdev-Ye-Kitaev model provides a solvable theory of entangled many-particle quantum states without quasiparticle excitations. I will describe how its solution has led to an understanding of the universal structure of the low energy density of states of charged black holes, and to realistic and universal models of strange metals.

Study of Effective 2+1 Dimensional Gravity in Ferrofluid‐Based Hyperbolic Metamaterials

AbstractRecent theoretical and experimental work demonstrated that nonlinear optics of ferrofluid‐based hyperbolic metamaterials exhibit very unusual spatiotemporal dynamics. Here a detailed theoretical and experimental study of mutual interactions of individual self‐focused optical filaments inside this metamaterial is reported. In agreement with theoretical expectations, the observed mutual interactions of individual filaments exhibit strong similarities with general relativity in 2+1 dimensions, which predicts that these interactions must have predominantly non‐Newtonian topological character. This observation is important since 2+1‐dimensional gravity is an exactly solvable theory even in the quantum gravity limit.

A solvable quantum field theory with asymptotic freedom in (3+1) dimensions

Recently, Ai, Bender and Sarkar gave a prescription on how to obtain [Formula: see text]-symmetric field theory results from an analytic continuation of Hermitian field theories. We perform this analytic continuation for the massless (critical) [Formula: see text] model with quartic interaction in (3+1) dimensions. In the large-[Formula: see text] limit, this theory is exactly solvable, and has negative [Formula: see text]-function in the ultraviolet, and a stable bound state in the infrared. The coupling diverges at a scale [Formula: see text], but can be continued into the far infrared. At finite temperature, the theory exhibits two phases separated by a second-order phase transition near [Formula: see text].

Describing metric-affine theories anew: alternative frameworks, examples and solutions

In this work we describe metric-affine theories anew by making a change of field variables. A series of equivalent frameworks is presented and identifications are worked out in detail. The advantage of applying the new frameworks is that any MAG theory can be handled as a Riemannian theory with additional fields. We study the Hilbert-Palatini action using the new field variables and disclose interesting symmetries under SO transformations in field space. Then, we use solvable and suitable Riemannian theories as seed models for solvable MAG theories, restricting ourselves to three examples. We present a black hole solution with torsion and non-metricity which under a certain tuning acquires a regular core. A de Sitter universe with the expansion powered by 3-form torsion, is also reported.

Extended analytical BCS theory of superconductivity in thin films

We present an analytically solvable theory of Bardeen-Cooper-Schrieffer-type superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. Closed-form expressions for the dependence of the superconducting critical temperature Tc as a function of the confinement size L are obtained, in quantitative agreement with experimental data with no adjustable parameters. Upon increasing the confinement, a crossover from a spherical Fermi surface, which contains two growing hollow spheres corresponding to states forbidden by confinement, to a strongly deformed Fermi surface, is predicted. This crossover represents a new topological transition, driven by confinement, between two Fermi surfaces belonging to two different homotopy classes. This topological transition provides a mechanistic explanation of the commonly observed non-monotonic dependence of Tc upon film thickness with a maximum which, according to our theory, coincides with the topological transition.

Gauge-Theoretic Origin of Rydberg Quantum Spin Liquids.

Recent atomic physics experiments and numerical works have reported complementary signatures of the emergence of a topological quantum spin liquid in models with blockade interactions. However, the specific mechanism stabilizing such a phase remains unclear. Here, we introduce an exact relation between an Ising-Higgs lattice gauge theory on the kagome lattice and blockaded models on Ruby lattices. This relation elucidates the origin of previously observed topological spin liquids by directly linking the latter to a deconfined phase of a solvable gauge theory. By means of exact diagonalization and unbiased quantum MonteCarlo simulations, we show that the deconfined phases extend in a broad region of the parameter space; these states are characterized by a large ground state overlap with resonating valence bond wave functions. These blockaded models include both creation or annihilation and hopping dynamics, and can be experimentally realized with Rydberg-dressed atoms, offering novel and controllable platforms for the engineering and characterization of spin liquid states.

Are the Zcs(3985) and Zcs(4000) the same state?

In this work, we focus on the great breakthroughs in BESIII and LHCb collaborations, the strange hidden charm tetraquarks Zcs(3985) and Zcs(4000). We aim to clarify the first and foremost question, whether they are the same state. The calculation is performed with a solvable nonrelativistic effective field theory which incorporates heavy quark spin symmetry, SU(3)F symmetry and possible violations comprehensively. Two experimentally accessible consequences with Zcs(3985) and Zcs(4000) as different states are presented, the existence of a tensor D¯s⁎D⁎ resonance and suppression of decay Zcs(3985) → J/ψK. The two predictions can be used to distinguish the two-state scheme from the one-state interpretation.

Pseudoparticle vertex solver for quantum impurity models

We present a quantum impurity solver based on a pseudo-particle framework, which combines diagrammatic resummations for a three-point vertex with diagrammatic Monte Carlo sampling of a four-point vertex. This recently proposed approach [A. J. Kim et al., arXiv:2112.15549] is generalized here to fermionic impurity problems and we discuss the technical details of the implementation, including the time-stepping approach, the Monte Carlo updates, and the routines for checking the two-particle irreducibility of the four-point vertex. We also explain how the vertex information can be efficiently stored using a Dubiner basis representation. The convergence properties of the algorithm are demonstrated with applications to exactly solvable impurity models and dynamical mean field theory simulations of the single-orbital Hubbard model. It is furthermore shown that the algorithm can handle a two-orbital problem with off-diagonal hybridizations, which would cause a severe sign problem in standard hybridization-expansion Monte Carlo simulations. Since the vertex-based algorithm successfully handles sign oscillating integrals in equilibrium and samples only connected diagrams, it may be a promising approach for real-time simulations.

Solvable theory of a strange metal at the breakdown of a heavy Fermi liquid

We introduce an effective theory for quantum critical points (QCPs) in heavy fermion systems, involving a change in carrier density without symmetry breaking. Our new theory captures a strongly coupled metallic QCP, leading to robust marginal Fermi liquid transport phenomenology, and associated linear in temperature ($T$) "strange metal" resistivity, all within a controlled large $N$ limit. In the parameter regime of strong damping of emergent bosonic excitations, the QCP also displays a near-universal "Planckian" transport lifetime, $\tau_{\mathrm{tr}}\sim\hbar/(k_BT)$. This is contrasted with the conventional so-called "slave boson" theory of the Kondo breakdown, where the large $N$ limit describes a weak coupling fixed point and non-trivial transport behavior may only be obtained through uncontrolled $1/N$ corrections. We also compute the weak-field Hall coefficient within the effective model as the system is tuned across the transition. We further find that between the two plateaus, reflecting the different carrier densities in the two Fermi liquid phases, the Hall coefficient can develop a peak in the critical crossover regime, like in recent experimental findings, in the parameter regime of weak boson damping.

Analysis of virtual meson production in a ( 1+1 )-dimensional scalar field model

Light-front time-ordered amplitudes are investigated in the virtual scalar meson production process in (1+1) dimensions using the solvable scalar field theory extended from the conventional Wick-Cutkosky model. There is only one Compton form factor (CFF) in the (1+1) dimensional computation of the virtual meson production process, and we compute both the real and imaginary parts of the CFF for the entire kinematic regions of $Q^2>0$ and $t<0$. We then analyze the contribution of each and every light-front time-ordered amplitude to the CFF as a function of $Q^2$ and $t$. In particular, we discuss the significance of the "cat's ears" contributions for gauge invariance and the validity of the "handbag dominance" in the formulation of the generalized parton distribution (GPD) function used typically in the analysis of deeply virtual meson production processes. We explicitly derive the GPD from the "handbag" light-front time-ordered amplitudes in the $-t/Q^2<<1$ limit and verify that the integrations of the GPD over the light-front longitudinal momentum fraction for the DGLAP and ERBL regions correspond to the valence and nonvalence contributions of the electromagnetic form factor that we have recently reported [Phys. Rev. D $\textbf{103}$, 076002 (2021)]. We also discuss the correspondence of the GPD to the parton distribution function for the analysis of the deep inelastic lepton-hadron scattering process and the utility of the new light-front longitudinal spatial variable $\tilde{z}$.

Ising model close to d=2

The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and analytical conformal bootstrap methods in Lorentzian signature, we show that the leading corrections to the Ising data are more singular than $\epsilon$. There must be infinitely many new states due to the $d$-dependence of conformal symmetry. The linear independence of conformal blocks is central to this bootstrap approach, which can be extended to more rigorous studies of non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.

Analytical theory of enhanced Bose–Einstein condensation in thin films

We present an analytically solvable theory of Bose–Einstein condensation (BEC) in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness L is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature T c ∼ L −1/2. For cold Bose gases, this implies an enhancement up to two orders of magnitude in T c for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. C ∼ T 2, is predicted for nano-scale films, which implies a different λ-point behavior with respect to bulk systems, while the condensate fraction is predicted to follow a law.

Plate theories: A‐priori fulfillment of the local conditions by the consistent‐approximation approach

AbstractClassical plates theories, like Kirchhoff's plate theory [1], are based on kinematical a‐priori assumptions. Avoiding these assumptions, we derive from the three‐dimensional theory of linear elasticity by means of Taylor‐series expansions the quasi two‐dimensional problem. This problem consists of infinitely many partial‐differential equations (PDEs) written in infinitely many displacement coefficients. With the consistent approximation approach we arrive at solvable hierarchical plate theories. By using the modular structure of the displacements coefficients (modularity), we obtain from these generic‐plate theories the complete‐plate theories, whose results fulfill the strong form of the local equilibrium conditions and the Neumann boundary conditions on the upper and lower face of the plate (local conditions) a‐priori. Furthermore, we show that every variable of the complete‐plate theories can be calculated.

Benign ghosts in higher-derivative systems

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. This happens, in particular, in exactly solvable higher-derivative theories, but exact solvability seems to be a sufficient but not a necessary condition for the benign nature of the ghosts.We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

Implications of the [formula omitted] and [formula omitted] as two different states

Recently, the hidden charm tetraquark states Zcs(3985) and Zcs(4000) with strangeness were observed by the BESIII and LHCb collaborations, respectively, which are great breakthroughs for exploring exotic quantum chromodynamics (QCD) structures. The first and foremost question is whether they are the same state. In this work, we explore the implications of the narrower state Zcs(3985) in BESIII and the wider one Zcs(4000) in LHCb as two different states. Within a solvable nonrelativistic effective field theory, we include the possible violations of heavy quark spin symmetry and SU(3) flavor symmetry in a comprehensive approach. If Zcs(3985) and Zcs(4000) are two different states, our results show that Zcs(4000)/Zcs(3985) is the pure (|D‾s∗D〉+/-|D‾sD∗〉)/2 state, and the SU(3) flavor partner of Zc(3900) is Zcs(4000) rather than the Zcs(3985). Another two important consequences are the existence of a tensor D‾s∗D∗ resonance with mass about 4126 MeV and width 13 MeV, and the suppression of the decay mode Zcs(3985)→J/ψK. The two consequences can be tested in experiments and distinguish the two-state interpretation from the one-state scheme.

Time glass: A fractional calculus approach

Out of equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide the first description for the recently conjectured Time Glasses using fractional calculus methods. An exactly solvable effective theory is introduced, with a continuous parameter describing the transition from liquid through normal glass, Time Glass, into the Gardner phase. The phenomenological description with a fractional Langevin equation is connected to a microscopic model of a particle in a sub-Ohmic bath in the framework of a generalized Caldeira-Leggett model.

Resonant particle creation by a time-dependent potential in a nonlocal theory

Considering an exactly solvable local quantum theory of a scalar field interacting with a δ-shaped time-dependent potential we calculate the Bogoliubov coefficients analytically and determine the spectrum of created particles. We then show how these considerations, when suitably generalized to a specific nonlocal “infinite-derivative” quantum theory, are impacted by the presence of nonlocality. In this model, nonlocality leads to a significant resonant amplification of certain modes, leaving its imprint not only in the particle spectrum but also in the total number density of created particles.

Vortex sheet turbulence as solvable string theory

We study steady vortex sheet solutions of the Navier–Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the tangent discontinuity of the local velocity parametrized as [Formula: see text]. This observation means that the steady flow represents the low-temperature limit of the Gibbs distribution for vortex sheet dynamics with the normal displacement [Formula: see text] of the vortex sheet as a Hamiltonian coordinate and [Formula: see text] as a conjugate momentum. An infinite number of Euler conservation laws lead to a degenerate vacuum of this system, which explains the complexity of turbulence statistics and provides the relevant degrees of freedom (random surfaces). The simplest example of a steady solution of the Navier–Stokes equation in the turbulent limit is a spherical vortex sheet whose flow outside is equivalent to a potential flow past a sphere, while the velocity is constant inside the sphere. Potential flow past other bodies provide other steady solutions. The new ingredient we add is a calculable gap in tangent velocity, leading to anomalous dissipation. This family of steady solutions provides an example of the Euler instanton advocated in our recent work, which is supposed to be responsible for the dissipation of the Navier–Stokes equation in the turbulent limit. We further conclude that one can obtain turbulent statistics from the Gibbs statistics of vortex sheets by adding Lagrange multipliers for the conserved volume inside closed surfaces, the rate of energy pumping, and energy dissipation. The effective temperature in our Gibbs distribution goes to zero as [Formula: see text] with Reynolds number [Formula: see text] in the turbulent limit. The Gibbs statistics in this limit reduces to the solvable string theory in two dimensions (so-called [Formula: see text] critical matrix model). This opens the way for nonperturbative calculations in the Vortex Sheet Turbulence, some of which we report here.

Emergence of generalized hydrodynamics in the non-local Luttinger model

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed.

Page curve for an evaporating black hole

A Page curve for an evaporating black hole in asymptotically flat spacetime is computed by adapting the Quantum Ryu-Takayanagi (QRT) proposal to an analytically solvable semi-classical two-dimensional dilaton gravity theory. The Page time is found to be one third of the black hole lifetime, at leading order in semi-classical corrections. A Page curve is also obtained for a semi-classical eternal black hole, where energy loss due to Hawking evaporation is balanced by an incoming energy flux.