Examinando por Materia "Sistemas cuánticos"

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    On the tensorial structure of the generalized eigenstate thermalization hypothesis
    (Universidad del Valle, 2025) Campos Muñoz, Krystifer; Madronero, Javier
    In this work, we focus on the Eigenstate Thermalization Hypothesis (ETH) [1] as a leading explanation for the emergence of thermal behavior in many-body quantum systems. We discuss recent advances in the field, particularly the work of Silvia, Laura, and Jorge [2,3], who extended the ETH to include multipoint thermal correlation functions. Their findings revealed a direct connection between these correlations and the cumulants of free probability [4]. This connection, along with the free independence condition, suggests the existence of subleading contributions not captured by the generalized ETH and free probability. To support this idea, we analytically computed the subleading contributions for the two-point correlation functions in a system of random free fermions; for that, we used quantum information and random matrix theory techniques that include quantum channels, Gaussian ensembles and Haar averages. Our results confirmed our initial hypothesis: the subleading contributions contain relevant information about the presence or absence of time-reversal symmetry in the system considered.
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    Tensor network-based ansatz for the analysis of a spin-1 system quadrupolar phases
    (Universidad del Valle, 2024) Enríquez Zamudio, Ana María; Rodriguez-Ramirez, Karen
    The precision achieved by experimental techniques with ultracold atoms has enabled the creation of quantum simulators, facilitating the exploration of one-dimensional systems in the laboratory. In these systems, fluctuations are inherently collective and propagate over large distances due to frequent collisions. As a result, theoretical frameworks have been developed that leverage these fluctuations to describe such systems. Ultracold gases confined in optical lattices not only serve as quantum simulators for traditional condensed matter systems but also act as platforms to create new many-body quantum systems. In this work, two numerical techniques are proposed to explore a spin-1 bosonic gas contained in a one-dimensional optical lattice, in the strongly interacting phase and in the Mott insulator regime. The first technique is a mean-field approach, known as the Gutzwiller ansatz, which approximates the many-body wave function as the product of individual contributions at each site. Additionally, a more advanced ansatz has been developed that considers pairs of coupled sites, allowing for the exploration of regions in the phase space that are not accessible with the traditional ansatz. The second technique is based on tensor networks, specifically representing the state as a Matrix Product State (MPS), combined with the Time-Evolving Block Decimation (TEBD) algorithm. This technique is used to analyze the ground state properties and magnetic behavior of the system under the influence of an external magnetic field. Both techniques were evaluated within the context of a Bilinear-Biquadratic Heisenberg Hamiltonian, incorporating perturbative corrections to account for the quadratic Zeeman effect. The results of this work demonstrate that tensor networks, particularly MPS, provide a robust numerical technique for capturing the quantum phenomena exhibited by spin-1 bosons. The calculations of ground state energy and magnetization profiles confirm the effectiveness of tensor networks in representing the essential physics of the system. Furthermore, the investigation of entanglement properties reveals that the system’s entanglement entropy obeys an area law, characteristic of gapped one-dimensional systems. Chirality and spin correlation observables were also explored, revealing relevant information about the system’s behavior under various interaction parameters. The results are consistent with previous theoretical and numerical studies, highlighting the potential of tensor networks to address challenges in many-body quantum physics. This work introduces a novel numerical perspective within the context of Solid State research at the University of Valle, paving the way for future studies utilizing advanced tensor network techniques.