Publications

Order by: publication date number of citations

• Position operators and interband matrix elements of scalar and vector potentials in the 8-band Kane model

  I. A. Ado, M. Titov, Rembert A. Duine, Arne Brataas

  SciPost Phys. 17, 009 (2024) · published 10 July 2024 | Toggle abstract · pdf

  We diagonalize the 8-band Kane Hamiltonian with a proper inclusion of the interband matrix elements of the scalar and vector potentials. This leads, among other results, to a modification of the conventional expression for the spin-orbit coupling (SOC) strength in narrow-gap semiconductors with the zinc blende symmetry. We find that in GaAs, at low temperatures, the correct expression for the SOC strength is actually twice as large as usually considered. In InSb it is $1.76$ times larger. We also provide a proper treatment of the interband matrix elements of the position operator. We show that the velocity operator in a crystal should be defined as a time-derivative of a fictitious position operator rather than the physical one. We compute the expressions for both these position operators projected to the conduction band of the 8-band Kane model. We also derive an expression for the projected velocity operator and demonstrate that the SOC strength in it differs from the SOC strength in the Hamiltonian. The ratio between them is not equal to $1$, as it is often assumed for the Rashba model. It does not equal $2$ either. The correct result for this ratio is given by a rational function of the parameters of the model. This function takes values between $4(23+3\sqrt{2})/73≈ 1.49$ and $2$. Our findings modify a vast number of research results obtained using the Rashba model and provide a path for consistent treatment of the latter in future applications.

• Integrable deformations from twistor space

  Lewis T. Cole, Ryan A. Cullinan, Ben Hoare, Joaquin Liniado, Daniel C. Thompson

  SciPost Phys. 17, 008 (2024) · published 10 July 2024 | Toggle abstract · pdf

  Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory.

• Prethermalization in coupled one-dimensional quantum gases

  Maciej Łebek, Miłosz Panfil, Robert M. Konik

  SciPost Phys. 17, 007 (2024) · published 10 July 2024 | Toggle abstract · pdf

  We consider the problem of the development of steady states in one-dimensional Bose gas tubes that are weakly coupled to one another through a density-density interaction. We analyze this development through a Boltzmann collision integral approach. We argue that when the leading order of the collision integral, where single particle-hole excitations are created in individual gases, is dominant, the state of the gas evolves first to a non-thermal fixed point, i.e. a prethermalization plateau. This order is dominant when a pair of tubes are inequivalent with, say, different temperatures or different effective interaction parameters, $\gamma$. When both tubes are in the strongly interacting regime we additionally characterize this non-thermal prethermalization plateau by constructing the quasi-conserved quantities that control the existence of this plateau as well as the associated generalized Gibbs ensemble.

• disorder: Deep inelastic scattering at high orders

  Alexander Karlberg

  SciPost Phys. Codebases 32 (2024) · published 9 July 2024 | Toggle abstract · pdf

  We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing $\mathcal{O}(\alpha_{\mathrm{s}}^2)$ dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to $\mathcal{O}(\alpha_{\mathrm{s}}^3)$.

  1 citation

• Codebase release r1.0 for disorder

  Alexander Karlberg

  SciPost Phys. Codebases 32-r1.0 (2024) · published 9 July 2024 | Toggle abstract · src

  We present a Fortran 77/95 code capable of computing QCD corrections in deep inelastic scattering (DIS). The code uses the Projection-to-Born method to augment an existing $\mathcal{O}(\alpha_{\mathrm{s}}^2)$ dijet DIS code, thereby obtaining predictions for photon-mediated neutral-current single-jet DIS production in the laboratory frame. The code is lightweight and fast, and yet includes the most common functionalities found in typical perturbative QCD programs, like automatic renormalisation and factorisation scale uncertainties, options to run and combine multiple seeds, and interfaces to fastjet and LHAPDF. Due to the underlying disent and HOPPET codes, the program also provides stable results in the infrared, relevant for extracting logarithmic coefficients for analytic resummations, and access to the massless DIS structure functions and (reduced) cross sections up to $\mathcal{O}(\alpha_{\mathrm{s}}^3)$.

  1 citation

• Spectral solutions for the Schrödinger equation with a regular singularity

  Pushkar Mohile, Ayaz Ahmed, T. R. Vishnu, Pichai Ramadevi

  SciPost Phys. Core 7, 041 (2024) · published 5 July 2024 | Toggle abstract · pdf

  We propose a modification in the Bethe-like ansatz to reproduce the hydrogen atom spectrum and the wave functions. Such a proposal provided a clue to attempt the exact quantization condition (EQC) for the quantum periods associated with potentials $V(x)$ which are of the form $(V(x) = |x| + a/|x| + b/|x|^2 )$. We validate the EQC proposal by showing that our computed Voros spectrum in the limit $a,b → 0$ is matching well with the true spectrum of the familiar $|x|$ potential. Thus we have given a route to obtain the spectral solution for the one dimensional Schrödinger equation involving potentials with regular singularity at the origin.

• Off-shell strings II: Black hole entropy

  Amr Ahmadain, Aron C. Wall

  SciPost Phys. 17, 006 (2024) · published 5 July 2024 | Toggle abstract · pdf

  In 1994, Susskind and Uglum argued that it is possible to derive the Bekenstein-Hawking entropy $A/4G_N$ from string theory. In this article we explain the conceptual underpinnings of this argument, while elucidating its relationship to induced gravity and ER=EPR. Following an off-shell calculation by Tseytlin, we explicitly derive the classical closed string effective action from sphere diagrams at leading order in $\alpha^{\prime}$. We then show how to use this to obtain black hole entropy from the RG flow of the NLSM on conical manifolds. (We also briefly discuss the more problematic "open string picture" of Susskind and Uglum, in which strings end on the horizon.) We then compare these off-shell results with the rival "orbifold replica trick" using the on-shell $\mathbb{C}/Z_{N}$ background, which does not account for the leading order Bekenstein-Hawking entropy-unless perhaps tachyons are allowed to condense on the orbifold. Possible connections to the ER=EPR conjecture are explored. Finally, we discuss prospects for various extensions, including prospects for deriving holographic entanglement entropy in the bulk of AdS.

  1 citation

• Off-shell strings I: S-matrix and action

  Amr Ahmadain, Aron C. Wall

  SciPost Phys. 17, 005 (2024) · published 5 July 2024 | Toggle abstract · pdf

  We explain why Tseytlin's off-shell formulation of string theory is well-defined. Although quantizing strings on an off-shell background requires an arbitrary choice of Weyl frame, this choice is not physically significant since it can be absorbed into a field redefinition of the target space fields. The off-shell formalism is particularly subtle at tree-level, due to the treatment of the noncompact conformal Killing group SL(2,$\mathbb{C}$) of the sphere. We prove that Tseytlin's sphere prescriptions recover the standard tree-level Lorentzian S-matrix, and show how to extract the stringy $i\varepsilon$ prescription from the UV cutoff on the worldsheet. We also demonstrate that the correct tree-level equations of motion are obtained to all orders in perturbation theory in $g_s$ and $\alpha^{\prime}$, and illuminate the close connection between the string action and the c-theorem.

  1 citation

• Exact Mazur bounds in the pair-flip model and beyond

  Oliver Hart

  SciPost Phys. Core 7, 040 (2024) · published 4 July 2024 | Toggle abstract · pdf

  By mapping the calculation of Mazur bounds to the enumeration of walks on fractal structures, we present exact bounds on the late-time behavior of spin autocorrelation functions in models exhibiting pair-flip dynamics and more general $p$-flip dynamics. While the pair-flip model is known to exhibit strong Hilbert space fragmentation, the effect of its nontrivial conservation laws on autocorrelation functions has, thus far, only been calculated numerically, which has led to incorrect conclusions about their thermodynamic behavior. Here, using exact results, we prove that infinite-temperature autocorrelation functions exhibit infinite coherence times at the boundary, and that bulk Mazur bounds decay asymptotically as $1/\sqrt{L}$, rather than $1/L$, as had previously been thought. This result implies that the nontrivial conserved operators implied by $p$-flip dynamics have an important qualitative impact on bulk thermalization properties beyond the constraints imposed by the simple global symmetries of the models.

• THz higher-order topological photonics in Ge-on-Si heterostructures

  Ian Colombo, Pietro Minazzi, Emiliano Bonera, Fabio Pezzoli, Jacopo Pedrini

  SciPost Phys. Core 7, 039 (2024) · published 4 July 2024 | Toggle abstract · pdf

  We design germanium-based higher-order topological cavities for terahertz applications by breaking the symmetry of a two-dimensional photonic crystal following the Su-Schrieffer-Heeger model. Calculations demonstrate the parity inversion of the electric field in differently deformed unit cells. The interface between domains of opposite topology presents edge and corner modes. The former are chiral, locking light propagation to its helicity. The latter prove that Ge-based structures can be used as high-order topological photonic crystals. These findings can accelerate the development of Si-photonic components working in a spectral range of high technological interest.