On the out-of-equilibrium dynamics with tensor networks
[eng] Quantum many-body dynamics is a vast field of physics at the intersection of statistical mechanics, condensed matter, quantum information, and computational physics. Understanding the time evolution of observable correlations—such as those involved in material responses—is both a milestone for...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/224823 |
| Acceso en línea: | https://hdl.handle.net/2445/224823 http://hdl.handle.net/10803/696093 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria quàntica Mecànica estadística Quantum theory Statistical mechanics |
| Sumario: | [eng] Quantum many-body dynamics is a vast field of physics at the intersection of statistical mechanics, condensed matter, quantum information, and computational physics. Understanding the time evolution of observable correlations—such as those involved in material responses—is both a milestone for technological advancement and a corner-stone for generating fundamental knowledge. At the intersection of emergent collective behavior in many-body systems, quantum physics, and information theory lies the classical simulation of out-of-equilibrium phenomena. Without numerical tools, progress in disciplines that require heavy computations with high-dimensional vectors and matrices would be limited to purely analytical predictions and constrained by the available expertise and resources needed to build benchmarking experiments. The goal of this thesis is to advance the classical simulation of quantum many-body systems using Tensor Networks. This technique has proven fruitful for predicting equilibrium ground states and thermal properties of one-dimensional systems, yet it still faces challenges when applied to out-of-equilibrium scenarios. In brief, the dynamics of experimentally accessible expectation values can be represented as a 2D Tensor Network, which must be contracted using iterative methods such as Time-Evolving Block Decimation. However, the memory and computational time required for these calculations—which reflect the methods’ complexity—are known to grow exponentially with the simulated physical time in generic systems. This limitation is often referred to in the literature as the entanglement barrier. This manuscript tackles the problem through the three inequivalent ways in which the 2D Tensor Network can be contracted. In Chapter 3, we study how Schrödinger-picture contraction from the state edge of the network can be modified to improve the convergence of iterative contraction and reduce truncation errors in small systems. To this end, we explore physical decoherence in optimized bases and artificial generalized decoherence, finding that both alternatives show promise for new protocols that overcome the entanglement barrier. In Chapter 4, we explore Heisenberg-picture contraction from the observable edge, combining the concept of generalized decoherence with Pauli Weight truncation. By thoroughly characterizing the Pauli weight requirements to accurately describe the time evolution of local expectation values from initial product states, we conclude that truncating off-diagonal Pauli Weights is an effective scheme for simulating long-time dynamics—and we successfully implement it. We conclude with a spatial characterization of Pauli Weight spreading, bridging Tensor Network simulations and the field of operator hydrodynamics. Finally, in Chapter 5, we focus on the transverse contraction of the 2D Tensor Net-work using the light-cone algorithm, analyzing its variants in terms of truncation strategies and convergence across different models. This leads to a systematic characterization of the method based on the integrability of the underlying Hamiltonians and single-spin noise models. |
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