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- Bollmark, Gunnar, et al.
(författare)
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Dimensional crossover and phase transitions in coupled chains : Density matrix renormalization group results
- 2020
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Ingår i: Physical Review B. - : AMER PHYSICAL SOC. - 2469-9950 .- 2469-9969. ; 102:19
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Tidskriftsartikel (refereegranskat)abstract
- Quasi-one-dimensional (Q1D) systems, i.e., three- and two-dimensional (3D/2D) arrays composed of weakly coupled one-dimensional lattices of interacting quantum particles, exhibit rich and fascinating physics. They are studied across various areas of condensed matter and ultracold atomic lattice-gas physics, and are often marked by dimensional crossover as the coupling between one-dimensional systems is increased or temperature decreased, i.e., the Q1D system goes from appearing largely 1D to largely 3D. Phase transitions occurring along the crossover can strongly enhance this effect. Understanding these crossovers and associated phase transitions can be challenging due to the very different elementary excitations of 1D systems compared to higher-dimensional ones. In the present work, we combine numerical matrix product state (MPS) methods with mean-field (MF) theory to study paradigmatic cases of dimensional crossovers and the associated phase transitions in systems of both hard-core and soft-core lattice bosons, with relevance to both condensed matter physics and ultracold atomic gases. We show that the superfluid-to-insulator transition is a first order one, as opposed to the isotropic cases, and calculate transition temperatures for the superfluid states, finding excellent agreement with analytical theory. At the same time, our MPS + MF approach keeps functioning well where the current analytical framework cannot be applied. We further confirm the qualitative and quantitative reliability of our approach by comparison to exact quantum Monte Carlo calculations for the full 3D arrays.
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| 3. |
- Bollmark, Gunnar
(författare)
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Order in Strongly Correlated Quasi-One-Dimensional Systems : Solving Higher-Dimensional Systems Combining Matrix-Product-State Methods and Mean-Field Theory
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Since their discovery the understanding of unconventional superconductors (USCs) has posed a great challenge in condensed matter physics. One central problem, both of theory and experiment, lies in determining the microscopic origin of electron pairing in such systems. Partly, the difficulty lies in numerically simulating systems hypothesized to represent USCs. In particular, it remains an open question whether the ground state of the two-dimensional Hubbard model realizes an USC. This system epitomizes the combined difficulty of finding both whether electrons form pairs and whether they condense into an USCs phase.Conversely, the one-dimensional (1D) Hubbard ladder is readily solved numerically using matrix-product state (MPS) methods. Doped away from a half-filled lattice repulsively mediated electron pairing is realized in the system. However, quantum fluctuations hinder ordering in such systems even at zero temperature viz. continuous symmetries cannot be spontaneously broken. Instead, quasi-one-dimensional (Q1D) systems featuring arrays of one-dimensional (1D) chains weakly coupled into a higher-dimensional system can be studied. While pairing is resolved in each 1D system using MPS the condensation of such pairs into a superconductor may be treated using mean-field (MF) theory. The subject of this thesis is the development of the MPS+MF framework: An algorithm utilizing MPS and MF theory capable of solving Q1D systems.Developing new methods requires comparison with known solutions to learn of their potential inaccuracies. Thus, development is split into three steps: i) Simulation of bosons to test the basic approach, ii) simulation of attractive fermions, iii) simulation of an USC composed of repulsive Hubbard ladders. The first two targets admit comparison to quantum Monte Carlo simulations and, for some parameters, analytical methods. The MPS+MF framework is found to simulate the critical temperature of condensation with a fixed ratio to the true critical temperature, independent of Q1D coupling. Additionally, the framework is found capable of resolving competition of insulating and USC phases.Utilizing the possibility of evolving states in time using MPS numerics, MPS+MF is extended to perform self-consistent time evolution. We find that this method allows the detection of superconductivity out of equilibrium and, in particular, dynamically induced superconductivity.
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| 5. |
- Bollmark, Gunnar, et al.
(författare)
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Solving 2D and 3D lattice models of correlated fermions : combining matrix product states with mean-field theory
- 2023
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Ingår i: Physical Review X. - : American Physical Society. - 2160-3308. ; 13:1
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Tidskriftsartikel (refereegranskat)abstract
- Correlated electron states are at the root of many important phenomena including unconventional superconductivity (USC), where electron pairing arises from repulsive interactions. Computing the properties of correlated electrons, such as the critical temperature Tc for the onset of USC, efficiently and reliably from the microscopic physics with quantitative methods remains a major challenge for almost all models and materials. In this theoretical work, we combine matrix product states (MPS) with static mean field (MF) to provide a solution to this challenge for quasi-one-dimensional (Q1D) systems: two- and three-dimensional materials comprised of weakly coupled correlated 1D fermions. This MPS+MF framework for the ground state and thermal equilibrium properties of Q1D fermions is developed and validated for attractive Hubbard systems first, and further enhanced via analytical field theory. We then deploy it to compute Tc for superconductivity in 3D arrays of weakly coupled, doped, and repulsive Hubbard ladders. The MPS+MF framework thus enables the quantitative study of USC and high-Tc superconductivity—and potentially many more correlated phases—in fermionic Q1D systems based directly on their microscopic parameters, in ways inaccessible to previous methods. This approach further allows one to treat competing macroscopic orders, such as superconducting and insulating ones, on an equal footing. Benchmarks of the framework using auxiliary-field quantum Monte Carlo techniques show that the overestimation of, e.g., Tc due to its mean-field component, is near constant in microscopic parameters. These features of the MPS+MF approach to correlated fermions open up the possibility of designing deliberately optimized Q1D superconductors, from experiments in ultracold gases to synthesizing new materials.
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| 6. |
- Marten, Svenja, et al.
(författare)
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Transient superconductivity in three-dimensional Hubbard systems by combining matrix-product states and self-consistent mean-field theory
- 2023
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Ingår i: SciPost Physics. - : SciPost Foundation. - 2542-4653. ; 15:6
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Tidskriftsartikel (refereegranskat)abstract
- We combine matrix-product-state (MPS) and mean-field (MF) methods to model the real-time evolution of a three-dimensional (3D) extended Hubbard system formed from one-dimensional (1D) chains arrayed in parallel with weak coupling in-between them. This approach allows us to treat much larger 3D systems of correlated fermions out-of-equilibrium over a much more extended real-time domain than previous numerical approaches. We deploy this technique to study the evolution of the system as its parameters are tuned from a charge-density wave phase into the superconducting regime, which allows us to investigate the formation of transient non-equilibrium superconductivity. In our ansatz, we use MPS solutions for chains as input for a self-consistent time-dependent MF scheme. In this way, the 3D problem is mapped onto an effective 1D Hamiltonian that allows us to use the MPS efficiently to perform the time evolution, and to measure the BCS order parameter as a function of time. Our results confirm previous findings for purely 1D systems that for such a scenario a transient superconducting state can occur.
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