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| 2. |
- 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. |
- Dolfi, Michele, et al.
(författare)
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Matrix Product State applications for the ALPS project
- 2014
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Ingår i: Computer Physics Communications. - : Elsevier BV. - 0010-4655 .- 1879-2944. ; 185:12, s. 3430-3440
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Tidskriftsartikel (refereegranskat)abstract
- The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as part of the ALPS package, that provide an efficient and flexible implementation of these methods based on a matrix product state (MPS) representation. Our applications implement, within the same framework, algorithms to variationally find the ground state and low-lying excited states as well as simulate the time evolution of arbitrary one-dimensional and two-dimensional models. Implementing the conservation of quantum numbers for generic Abelian symmetries, we achieve performance competitive with the best codes in the community. Example results are provided for (i) a model of itinerant fermions in one dimension and (ii) a model of quantum magnetism. PROGRAM SUMMARY Program title: ALPS MPS Catalogue identifier: AEUL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Use of ‘mps optim’, ‘mps tevol’, ‘mps meas’ or ‘mps overlap’ requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. No. of lines in distributed program, including test data, etc.: 373799 No. of bytes in distributed program, including test data, etc.: 2019043 Distribution format: tar.gz Programming language: C++, OpenMP for parallelization. Computer: PC, HPC cluster. Operating system: Any, tested on Linux, Mac OS X and Windows. Has the code been vectorized or parallelized?: Parallelized using OpenMP 1 to 24 processors used. RAM: 100 MB–100 GB. Classification: 7.7. External routines: ALPS [1, 2], BLAS/LAPACK, HDF5. Nature of problem: Solution of quantum many-body systems is generally a hard problem. The many-body Hilbert space grows exponentially with the system size which limits exact diagonalization results to only 20–40 spins, and the fermionic negative sign problem limits the Quantum Monte Carlo methods to a few special cases. Solution method: The matrix product states ansatz provides a controllable truncation of the Hilbert space which makes it currently the method of choice to investigate low-dimensional systems in condensed matter physics. Our implementation allows simulation of arbitrary one-dimensional and two-dimensional models and achieves performance competitive with the best codes in the community. We implement conservation of quantum numbers for generic Abelian symmetries. Running time: 10 s–8h per sweep. References: [1] B. Bauer, et al. (ALPS Collaboration), The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. 2011 (05) (2011) P05001. http://dx.doi.org/10.1088/1742-5468/2011/05/P05001. [2] http://alps.comp-phys.org.
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| 7. |
- Dolfi, Michele, et al.
(författare)
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Minimizing nonadiabaticities in optical-lattice loading
- 2015
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 91:3
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Tidskriftsartikel (refereegranskat)abstract
- In the quest to reach lower temperatures of ultracold gases in optical-lattice experiments, nonadiabaticities during lattice loading represent one of the limiting factors that prevent the same low temperatures being reached as in experiments without lattices. Simulating the loading of a bosonic quantum gas into a one-dimensional optical lattice with and without a trap, we find that the redistribution of atomic density inside a global confining potential is by far the dominant source of heating. Based on these results we propose adjusting the trapping potential during loading to minimize changes to the density distribution. Our simulations confirm that a very simple linear interpolation of the trapping potential during loading already significantly decreases the heating of a quantum gas, and we discuss how loading protocols minimizing density redistributions can be designed.
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| 8. |
- Dupont, M., et al.
(författare)
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Monolayer CrCl3 as an Ideal Test Bed for the Universality Classes of 2D Magnetism
- 2021
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 127:3
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Tidskriftsartikel (refereegranskat)abstract
- The monolayer halides CrX3 (X = Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl3 has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl3 for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl3, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl3 to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.
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| 9. |
- Fukuhara, Takeshi, et al.
(författare)
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Quantum dynamics of a mobile spin impurity
- 2013
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Ingår i: Nature Physics. - : Nature Publishing Group. - 1745-2473 .- 1745-2481. ; 9:4, s. 235-241
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Tidskriftsartikel (refereegranskat)abstract
- One of the elementary processes in quantum magnetism is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, the quantum-coherent propagation of a magnetic excitation in the Heisenberg model can be observed using a post-selection technique. Extending the study to the superfluid regime of the bath, we quantitatively determine how the bath affects the motion of the impurity, showing evidence of polaronic behaviour. The experimental data agree with theoretical predictions, allowing us to determine the effect of temperature on the impurity motion. Our results provide a new approach to studying quantum magnetism, mobile impurities in quantum fluids and polarons in lattice systems.
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| 10. |
- Kamar, Naushad Ahmad, et al.
(författare)
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Dynamics of a mobile impurity in a two-leg bosonic ladder
- 2019
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 100:2
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the behavior of a mobile quantum impurity, restricted to a one-dimensional motion, in a bath formed by a two-leg bosonic ladder through a combination of field theory [Tomonaga-Luttinger liquid (TLL)] and numerical (density-matrix renormalization group) techniques. We compute the Green's function of the impurity as a function of time at different momenta. We find a power-law decay at zero momentum, which signals the breakdown of a quasiparticle description of the impurity motion. We compute the exponent both for the limits of weak and strong impurity-bath interactions. At small impurity-bath interaction, the impurity experiences the ladder as a single channel one-dimensional bath, but with an effective coupling reduced by a factor of root 2. We compare the numerical results for the exponent at zero momentum with a semianalytical expression, initially established for the chain, and find excellent agreement without adjustable parameters. We find an increase of the exponent with increasing transverse tunneling in the bath. At small tunneling, the exponent is compatible with the TLL prediction, while larger tunneling shows strong deviations. Finally, we show that, as a function of the momentum of the impurity, two different regimes of decay of the Green's function exist, similar to the single chain case. The power-law regime occurs for small momentum, while at large momentum the Green's function shows a faster decay, corresponding to the one expected in a polaronic regime. In this last regime, we compute the lifetime of the polaron numerically. We compute the critical momentum marking the transition between these two regimes. We compare with analytical predictions based on the structure factor of the bath and find good agreement with the numerical results. Finally, we discuss the consequences of our results for cold atomic experiments.
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