Publications

Order by: publication date number of citations

Topological insulators and geometry of vector bundles

Alexander S. Sergeev

SciPost Phys. Lect. Notes 67 (2023) · published 12 April 2023 | · pdf

For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of eigenspaces determines the electric polarization, while their global twisting gives rise to the metallic surface states in topological insulators. These phenomena are central topics of the present notes. The shape of eigenspaces is also responsible for many intriguing physical analogies, which have their roots in the theory of vector bundles. We give an informal introduction to the geometry and topology of vector bundles and describe various physical models from this mathematical perspective.
Time evolution of effective central charge and signatures of RG irreversibility after a quantum quench

Axel Cortes Cubero

SciPost Phys. 4, 016 (2018) · published 27 March 2018 | · pdf

At thermal equilibrium, the concept of effective central charge for massive deformations of two-dimensional conformal field theories (CFT) is well understood, and can be defined by comparing the partition function of the massive model to that of a CFT. This temperature-dependent effective charge interpolates monotonically between the central charge values corresponding to the IR and UV fixed points at low and high temperatures, respectively. We propose a non-equilibrium, time-dependent generalization of the effective central charge for integrable models after a quantum quench, $c_{\rm eff}(t)$, obtained by comparing the return amplitude to that of a CFT quench. We study this proposal for a large mass quench of a free boson, where the charge is seen to interpolate between $c_{\rm eff}=0$ at $t=0$, and $c_{\rm eff}\sim 1$ at $t\to\infty$, as is expected. We use our effective charge to define an "Ising to Tricritical Ising" quench protocol, where the charge evolves from $c_{\rm eff}=1/2$ at $t=0$, to $c_{\rm eff}=7/10$ at $t\to\infty$, the corresponding values of the first two unitary minimal CFT models. We then argue that the inverse "Tricritical Ising to Ising" quench is impossible with our methods. These conclusions can be generalized for quenches between any two adjacent unitary minimal CFT models. We finally study a large mass quench into the "staircase model" (sinh-Gordon with a particular complex coupling). At short times after the quench, the effective central charge increases in a discrete "staircase" structure, where the values of the charge at the steps can be computed in terms of the central charges of unitary minimal CFT models. When the initial state is a pure state, one always finds that $c_{\rm eff}(t\to\infty)\geq c_{\rm eff}(t=0)$, though $c_{\rm eff}(t)$, generally oscillates at finite times. We explore how this constraint may be related to RG flow irreversibility.
Ergodic Archimedean dimers

Henrik Schou Røising, Zhao Zhang

SciPost Phys. Core 6, 054 (2023) · published 11 August 2023 | · pdf

We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.
An exact local mapping from clock-spins to fermions

Simone Traverso, Christoph Fleckenstein, Maura Sassetti, Niccolò Traverso Ziani

SciPost Phys. Core 6, 055 (2023) · published 15 August 2023 | · pdf

Clock-spin models are attracting great interest, due to both their rich phase diagram and their connection to parafermions. In this context, we derive an exact local mapping from clock-spin to fermionic partition functions. Such mapping, akin to techniques introduced by Fedotov and Popov for spin $\frac{1}{2}$ chains, grants access to well established numerical tools for the perturbative treatment of fermionic systems in the clock-spin framework. Moreover, in one dimension, it allows to use bosonization to access the low energy properties of clock-spin models. Finally, aside from the direct application in clock-spin models, this new mapping enables the conception of interesting fermionic models, based on the clock-spin counterparts.
Resonating valence bonds and spinon pairing in the Dicke model

R. Ganesh, L. Theerthagiri, G. Baskaran

SciPost Phys. 4, 044 (2018) · published 30 June 2018 | · pdf

Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $\vert 0 \rangle$ and $\vert 1 \rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets of the form $\frac{1}{\sqrt{2}}[\vert 0 1 \rangle - \vert 1 0 \rangle]$. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or `spinons'. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to a mixed quantum state with a fluctuating number of spinon pairs -- an inchoate superconductor. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization ($M-N$), the emission exhibits a continuous transition from a dark state to a bright state. This is reflected in the spinon pair number distribution which can be tuned from sub-poissonian to super-poissonian regimes. This opens an exciting route to simulate RVB states and superconductivity.
Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

Tomáš Brauner, Naoki Yamamoto, Ryo Yokokura

SciPost Phys. 16, 051 (2024) · published 20 February 2024 | · pdf

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.
Noise-induced transport in the Aubry-André-Harper model

Devendra Singh Bhakuni, Talía L. M. Lezama, Yevgeny Bar Lev

SciPost Phys. Core 7, 023 (2024) · published 26 April 2024 | · pdf

We study quantum transport in a quasiperiodic Aubry-André-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which in the localized phase, captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.
$\Delta$S$^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C$_{60}$: Origin and the role of symmetry

Nikolaos P. Konstantinidis

SciPost Phys. 15, 037 (2023) · published 31 July 2023 | · pdf

The quantum antiferromagnetic Heisenberg model on the fullerene C$_{60}$ in a magnetic field has $4s$ ground-state magnetization discontinuities with $\Delta S^z=2$ as a function of the spin quantum number $s$ that disappear at the classical limit. The molecule can be seen as the fullerene C$_{20}$ with interpentagon interactions that generate the discontinuities when sufficiently strong. The discontinuities originate from the antiferromagnetic Ising limit for both molecules. The results show how spatial symmetry dictates the magnetic response of the $I_h$ fullerene molecules.
Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

Francisco M. O. Brito, Aires Ferreira

SciPost Phys. Core 7, 006 (2024) · published 21 February 2024 | · pdf

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.
Proximity-induced gapless superconductivity in two-dimensional Rashba semiconductor in magnetic field

Serafim S. Babkin, Andrew P. Higginbotham, Maksym Serbyn

SciPost Phys. 16, 115 (2024) · published 1 May 2024 | · pdf

Two-dimensional semiconductor-superconductor heterostructures form the foundation of numerous nanoscale physical systems. However, measuring the properties of such heterostructures, and characterizing the semiconductor in-situ is challenging. A recent experimental study by [Phys. Rev. Lett. 128, 107701 (2022)] was able to probe the semiconductor within the heterostructure using microwave measurements of the superfluid density. This work revealed a rapid depletion of superfluid density in semiconductor, caused by the in-plane magnetic field which in presence of spin-orbit coupling creates so-called Bogoliubov Fermi surfaces. The experimental work used a simplified theoretical model that neglected the presence of non-magnetic disorder in the semiconductor, hence describing the data only qualitatively. Motivated by experiments, we introduce a theoretical model describing a disordered semiconductor with strong spin-orbit coupling that is proximitized by a superconductor. Our model provides specific predictions for the density of states and superfluid density. Presence of disorder leads to the emergence of a gapless superconducting phase, that may be viewed as a manifestation of Bogoliubov Fermi surface. When applied to real experimental data, our model showcases excellent quantitative agreement, enabling the extraction of material parameters such as mean free path and mobility, and estimating $g$-tensor after taking into account the orbital contribution of magnetic field. Our model can be used to probe in-situ parameters of other superconductor-semiconductor heterostructures and can be further extended to give access to transport properties.

Previous 1 ... 80 81 82 83 84 85 86 87 88 89 90 Next