arXiv subjects

Manuel Calixto

Publications and source records attributed to Manuel Calixto.

At least 19 recordsLinked to original sources

arXiv2026

Real and momentum space analysis of topological phases in 2D d-wave altermagnets

Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength ($t_a^C$). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent ``steering'' effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering a robust alternative to traditional Chern number calculations, without relying on translational symmetry. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for ``edgetronics'' in altermagnetic materials, paving the way for next-generation, high-speed spintronic and ``spin-splitter'' logic devices and architectures.

cond-mat.mes-hall↗

arXiv2025

Highly robust logical qubit encoding in an ensemble of V-symmetrical qutrits

We propose using even and odd Sch\"odinger cat states formed from coherent states of U(3) of an ensemble of qutrits with a symmetrical V-configuration (a qubit-disguised qutrit) to encode a logical qubit. These carefully engineered logical qubit states are parameter independent stationary states of the effective master equation governing the evolution of the ensemble and, consequently, constitute dark states and are invulnerable to dissipation and correlated collective dephasing. In particular, the logical qubit states are immune to single qutrit decay (the analogous of single photon loss process for qutrits) and simultaneous decay and driving of two qutrits (the analogous two-photon loss and driving processes for qutrits). In addition, we show how to implement the single-qubit quantum NOT gate and the Hadamard gate followed by either the phase gate or the phase and $Z$ gates. We study analytically the case of two qutrits and conclude that the logical qubit states exhibit parity-sensitive inhomogeneous broadening and local correlated dephasing: the even logical state is completely immune to these processes, while odd one is vulnerable. Nevertheless, in the presence of these interactions one can also define another odd state with mixed permutation symmetry that is immune to both inhomogeneous broadening and local correlated dephasing. We suggest that these results can be extrapolated to an arbitrary number of qutrits. The effective master equation is deduced from a physical system composed of two parametrically coupled cavities with one of them interacting dispersively with an ensemble of three-level atoms (the qutrits). In principle this physical system can be implemented by means of two coplanar waveguide resonators, a SQUID parametrically coupling them, and a cloud of alkali atoms close to one of the resonators.

quant-ph↗

arXiv2025

Wigner quasi-probability distribution for symmetric multi-quDit systems and their generalized heat kernel

For a symmetric $N$-quDit system described by a density matrix $\rho$, we construct a one-parameter $s$ family $\mathcal{F}^{(s)}_\rho$ of quasi-probability distributions through generalized Fano multipole operators and Stratonovich-Weyl kernels. The corresponding phase space is the complex projective ${C}P^{D-1}=U(D)/U(D-1)\times U(1)$, related to fully symmetric irreducible representations of the unitary group $U(D)$. For the particular cases $D=2$ (qubits) and $D=3$ (qutrits), we analyze the phase-space structure of Schr\"odinger $U(D)$-spin cat (parity adapted coherent) states and we provide plots of the corresponding Wigner $\mathcal{F}^{(0)}_\rho$ function. We examine the connection between non-classical behavior and the negativity of the Wigner function. We also compute the generalized heat kernel relating two quasi-probability distributions $\mathcal{F}^{(s)}_\rho$ and $\mathcal{F}^{(s')}_\rho$, with $t=(s'-s)/2$ playing the role of ``time'', together with their twisted Moyal product in terms of a trikernel. In the thermodynamic limit $N\to\infty$, we recover the usual Gaussian smoothing for $s'>s$. A diagramatic interpretation of the phase-space construction in terms of Young tableaux is also provided.

quant-ph↗

arXiv2025

Lieb-Mattis ordering theorem of electronic energy levels in the thermodynamic limit

Lieb-Mattis theorem orders the lowest-energy states of total spin $s$ of a system of $P$ interacting fermions. We generalize these predictions to fermionic mixtures of $P$ particles with more than $N=2$ spinor components/species in the thermodynamic limit $P\to\infty$. The lowest-energy state inside each permutation symmetry sector $h$, arising in the $P$-fold tensor product decomposition, is well approximated by a U$(N)$ coherent (quasi-classical, variational) state, specially in the limit $P\to\infty$. In particular, the ground state of the system belongs the most symmetric (dominant Young tableau $h_0$) configuration. We exemplify our construction with the $N=3$ level Lipkin-Meshkov-Glick model, with a previous motivation on pairing correlations and U$(N)$-invariant quantum Hall ferromagnets. In the limit $P\to\infty$, each lowest-energy state within each permutation symmetry sector $h$ undergoes a quantum phase transition for a critical value $\lambda_c(h)$ of the exchange coupling constant $\lambda$, depending on $h$. This generalizes standard quantum phase transitions and their phase diagrams corresponding to the ground state belonging to the most symmetric sector $h_0$.

cond-mat.str-el↗

arXiv2024

Capturing magic angles in twisted bilayer graphene from information theory markers

Zero energy eigenstates $\psi_0(\theta)$ of the twisted bilayer graphene Hamiltonian at the Dirac point show a high sensitivity to the twist angle $\theta$ near the magic angles where the effective Fermi velocity vanishes. We use information theory markers, like fidelity-susceptibility and entanglement entropy of the reduced density matrix to the layer sector, to capture this quantum criticality of zero modes at magic twist angles.

cond-mat.mes-hall↗

arXiv2024

Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry

Quantum information measures are proposed to analyze the structure of near-gap electronic states in HgTe quantum wells in a strip geometry $(x,y)\in (-\infty,\infty)\times [0,L]$ of finite width $L$. This allows us to establish criteria for distinguishing edge from bulk states in the topological insulator phase, including the transition region and cutoff of the wave number $k_x$ where edge states degenerate with bulk states. Qualitative and quantitative information on the near-gap Hamiltonian eigenstates, obtained by tight-binding calculations, is extracted from localization measures, like the inverse participation ratio (IPR), entanglement entropies of the reduced density matrix (RDM) to the spin sector --measuring quantum correlations due to the spin-orbit coupling (SOC)-- and from correlation functions for a $y$-space partition. The analysis of IPR and entanglement entropies in terms of spin, wave number $k_x$ and position $y$, evidences a spin polarization structure and spatial confinement of near-gap wave functions at the boundaries $y=0,L$ and low $k_x$, as correspond to helical edge states. IPR localization measures provide momentum $k_x$ cutoffs from which near-gap states are no longer localized at the boundaries of the sample and become part of the bulk. Below this $k_x$-point cutoff, the entanglement entropy and the spin probabilities of the RDM also capture the spin polarization structure of edge states and exhibit a higher variability compared to the relatively low entropy of the bulk state region. For a real-space partition, the edge-state region in momentum space exhibits lower correlation modulus, but higher correlation arguments, than the bulk-state region.

cond-mat.mes-hall↗

arXiv2023

Localization measures of parity adapted U($D$)-spin coherent states applied to the phase space analysis of the $D$-level Lipkin-Meshkov-Glick model

We study phase-space properties of critical, parity symmetric, $N$-quDit systems undergoing a quantum phase transition (QPT) in the thermodynamic $N\to\infty$ limit. The $D=3$ level (qutrit) Lipkin-Meshkov-Glick (LMG) model is eventually examined as a particular example. For this purpose, we consider U$(D)$-spin coherent states (DSCS), generalizing the standard $D=2$ atomic coherent states, to define the coherent state representation $Q_\psi$ (Husimi function) of a symmetric $N$-quDit state $|\psi>$ in the phase space $\mathbb CP^{D-1}$ (complex projective manifold). DSCS are good variational aproximations to the ground state of a $N$-quDit system, specially in the $N\to\infty$ limit, where the discrete parity symmetry $\mathbb{Z}_2^{D-1}$ is spontaneously broken. For finite $N$, parity can be restored by projecting DSCS onto $2^{D-1}$ different parity invariant subspaces, which define generalized ``Schr\"odinger cat states'' reproducing quite faithfully low-lying Hamiltonian eigenstates obtained by numerical diagonalization. Precursors of the QPT are then visualized for finite $N$ by plotting the Husimi function of these parity projected DSCS in phase space, together with their Husimi moments and Wehrl entropy, in the neighborhood of the critical points. These are good localization measures and markers of the QPT.

quant-ph↗

arXiv2023

Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits

In this paper we study the entanglement in symmetric $N$-quDit systems. In particular we use generalizations to $U(D)$ of spin $U(2)$ coherent states and their projections on definite parity $\mathbb{C}\in\mathbb{Z}_2^{D-1}$ (multicomponent Schr\"odinger cat) states and we analyse their reduced density matrices when tracing out $M<N$ quDits. The eigenvalues (or Schmidt coefficients) of these reduced density matrices are completely characterized, allowing to proof a theorem for the decomposition of a $N$-quDit Schr\"odinger cat state with a given parity $\mathbb{C}$ into a sum over all possible parities of tensor products of Schr\"odinger cat states of $N-M$ and $M$ particles. Diverse asymptotic properties of the Schmidt eigenvalues are studied and, in particular, for the (rescaled) double thermodynamic limit ($N,M\rightarrow\infty,\,M/N$ fixed), we reproduce and generalize to quDits known results for photon loss of parity adapted coherent states of the harmonic oscillator, thus providing an unified Schmidt decomposition for both multi-quDits and (multi-mode) photons. These results allow to determine the entanglement properties of these states and also their decoherence properties under quDit loss, where we demonstrate the robustness of these states.

quant-ph↗

arXiv2021

Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models

In this paper we pursue the use of information measures (in particular, information diagrams) for the study of entanglement in symmetric multi-quDit systems. We use generalizations to U(D) of spin U(2) coherent states and their adaptation to parity (multicomponent Schr\"odinger cats) and we analyse one- and two-quDit reduced density matrices. We use these correlation measures to characterize quantum phase transitions occurring in Lipkin-Meshkov-Glick models of D=3-level identical atoms and we propose the rank of the corresponding reduced density matrix as a discrete order parameter.

quant-ph↗

arXiv2021

Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models

Collective spin operators for symmetric multi-quDit (namely, identical $D$-level atom) systems generate a U$(D)$ symmetry. We explore generalizations to arbitrary $D$ of SU(2)-spin coherent states and their adaptation to parity (multicomponent Schr\"odinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric $N$-quDit states, expressed in the last two cases in terms of collective U$(D)$-spin operator expectation values. Then we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin-Meshkov-Glick models of $3$-level identical atoms. We also propose an extension of the concept of SU(2) spin squeezing to SU$(D)$ and relate it to pairwise $D$-level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting $D$-level atom models.

quant-ph↗

arXiv2019

Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schr\"odinger cat states, defined as orthonormalized eigenstates of $k$-th powers of nonlinear $f$-oscillator annihilation operators, with $f$ of hypergeometric type. These "$k$-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states $|z_l\rangle, l=0,1,\dots,k-1$, with $z_l=z e^{2\pi i l/k}$ a $k$-th root of $z^k$, and they interpolate between number and coherent states. This fact motivates a continuous circle representation for high $k$. We also extend our study to truncated hypergeometric functions (finite dimensional Hilbert spaces) and a discrete exact circle representation is provided. We also show how to generate $k$-hypercats by amplitude dispersion in a Kerr medium and analyze their generalized Husimi $Q$-function in the super- and sub-Poissonian cases at different fractions of the revival time.

math-ph↗

arXiv2015

Some properties of Grassmannian $U(4)/U(2)^2$ coherent states and an entropic conjecture

We analyze mathematical and physical properties of a previously introduced [J. Phys. A47, 115302 (2014)] family of $U(4)$ coherent states (CS). They constitute a matrix version of standard spin $U(2)$ CS when we add an extra (pseudospin) dichotomous degree of freedom: layer, sublattice, two-well, nucleon, etc. Applications to bilayer quantum Hall systems at fractions of filling factor $\nu=2$ are discussed, where Haldane's sphere picture is generalized to a Grassmannian picture. We also extend Wehrl's definition of entropy from Glauber to Grassmannian CS and state a conjecture on the entropy lower bound.

math-ph↗

arXiv2015

Entropic uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials

Uncertainty relations are studied for a characterization of topological-band insulator transitions in 2D gapped Dirac materials isostructural with graphene. We show that the relative or Kullback-Leibler entropy in position and momentum spaces, and the standard variance-based uncertainty relation, give sharp signatures of topological phase transitions in these systems.

cond-mat.mes-hall↗

arXiv2013

Wavelet transform on the torus: a group theoretical approach

We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two dilations, which can be defined through the natural tensor product representation of usual wavelets on $\mathbb R$. Restricting ourselves to a single dilation imposes severe conditions for the mother wavelet that can be overcome by adding extra modular group $SL(2,\mathbb Z)$ transformations, thus leading to the concept of \emph{modular wavelets}. We define modular-admissible functions and prove frame conditions.

math-ph↗

arXiv2011

Almost Complete Coherent State Subsystems and Partial Reconstruction of Wave Functions in the Fock-Bargmann Phase-Number Representation

We provide (partial) reconstruction formulas and discrete Fourier transforms for wave functions in standard Fock-Bargmann (holomorphic) phase-number representation from a finite number $N$ of phase samples $\{θ_k=2πk/N\}_{k=0}^{N-1}$ for a given mean number $p$ of particles. The resulting Coherent State (CS) subsystem ${\cal S}=\{|z_k=p^{1/2}e^{iθ_k}>\}$ is complete (a frame) for truncated Hilbert spaces (finite number of particles) and reconstruction formulas are exact. For an unbounded number of particles, ${\cal S}$ is "almost complete" (a \textit{pseudo-frame}) and partial reconstruction formulas are provided along with an study of the accuracy of the approximation, which tends to be exact when $p<N$ and/or $N\to\infty$.

math-ph↗

arXiv2011

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.

math-ph↗

arXiv2011

Sampling Theorem and Discrete Fourier Transform on the Hyperboloid

Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from $N$ samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from $N$ samples is still possible and the accuracy of the approximation, which tends to be exact in the limit $N\to\infty$.

math-ph↗

arXiv2006

Wavelet Transform on the Circle and the Real Line: A Unified Group-Theoretical Treatment

We present a unified group-theoretical derivation of the Continuous Wavelet Transform (CWT) on the circle $\mathbb S^1$ and the real line $\mathbb{R}$, following the general formalism of Coherent States (CS) associated to unitary square integrable (modulo a subgroup, possibly) representations of the group $SL(2,\mathbb{R})$. A general procedure for obtaining unitary representations of a group $G$ of affine transformations on a space of signals $L^2(X,dx)$ is described, relating carrier spaces $X$ to (first or higher-order) ``polarization subalgebras'' ${\cal P}_X$. We also provide explicit admissibility and continuous frame conditions for wavelets on $\mathbb S^1$ and discuss the Euclidean limit in terms of group contraction.

math-ph↗