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Finite-temperature tensor network study of the Hubbard model on an infinite square lattice
Here, the Hubbard model is a longstanding problem in the theory of strongly correlated electrons and a very active one in the experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network—an infinite projected entangled pair state—evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With U(1)×U(1) symmetry and the bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators—measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit—provide evidence of disruption of the antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime.
Solving the Bethe-Salpeter equation in real frequencies at finite temperature
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Ab initio elasticity at finite temperature and stress in ferroelectrics
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In-medium similarity renormalization group at finite temperature
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Randall-Sundrum model with a dilaton field at finite temperature
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Anomalous gravitomagnetic moment and nonuniversality of the axial vortical effect at finite temperature
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Finite-temperature phase diagram of the Berenstein-Maldacena-Nastase matrix model on the lattice
We investigate the thermal phase structure of the Berenstein-Maldacena-Nastase matrix model using nonperturbative lattice Monte Carlo calculations. Our main analyses span 3 orders of magnitude in the coupling, involving systems with sizes up to 𝑁𝜏 =24 lattice sites and SU(𝑁) gauge groups with 8 ≤𝑁 ≤16. In addition, we carry out extended checks of discretization artifacts for 𝑁𝜏 ≤128 and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-𝑁 dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.
Finite-temperature many-body perturbation theory in the canonical ensemble
Benchmark data are presented for the zeroth- through third-order many-body perturbation corrections to the electronic Helmholtz energy, internal energy, and entropy in the canonical ensemble in a wide range of temperature. They are determined as numerical λ-derivatives of the respective quantities computed by thermal full configuration interaction with a perturbation-scaled Hamiltonian, $\hat{H} = \hat{H}_0 + λ\hat{V}$. Sum-over-states analytical formulas for up to the third-order corrections to these properties are also derived as analytical λ-derivatives. These formulas, which are verified by exact numerical agreement with the benchmark data, are given in terms of the Hirschfelder–Certain degenerate perturbation energies and should be valid for both degenerate and nondegenerate reference states at any temperature down to zero. Further, the results in the canonical ensemble are compared with the same in the grand canonical ensemble.
Velocity circulation intermittency in finite-temperature turbulent superfluid helium
We study intermittency of circulation moments in turbulent superfluid helium by using experimental grid turbulence and numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. More precisely, we compute the velocity circulation Γ r in loops of size r laying in the inertial range. For both experimental and numerical data, the circulation variance shows a clear Kolmogorov scaling < $Γ$$^2_r$ > ~ r 8/3 in the inertial range, independently of the temperature. Scaling exponents of high-order moments are comparable, within error bars, to previously reported anomalous circulation exponents in classical turbulence and low-temperature quantum turbulence numerical simulations.
Theory of the special displacement method for electronic structure calculations at finite temperature
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Almost strong zero modes at finite temperature
Interacting fermionic chains exhibit extended regions of topological degeneracy of their ground states as a result of the presence of Majorana or parafermionic zero modes localized at the edges. In the opposite limit of infinite temperature, the corresponding nonintegrable spin chains, obtained via generalized Jordan-Wigner mapping, are known to host so-called almost strong zero modes, which are long-lived with respect to any bulk excitations. Here we study the fairly unexplored territory that bridges these two extreme cases of zero and infinite temperature. We blend two established techniques for states, the Lanczos series expansion and a tensor network ansatz, uplifting them to the level of operator algebra. This allows us to efficiently simulate large system sizes for arbitrarily long timescales and to extract the temperature-dependent decay rates. We observe that for the Kitaev-Hubbard model, the decay rate of the edge mode depends exponentially on the inverse temperature 𝛽, and on an effective energy scale Δ eff that is greater than the thermodynamic gap of the system Δ.
Normal State Properties of Quantum Critical Metals at Finite Temperature
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Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
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On the holographic dual of a symmetry operator at finite temperature
Topological symmetry operators of holographic large 𝑁 CFT 𝐷 ’s are dual to dynamical branes in the gravity dual AdS 𝐷+1 . We use this correspondence to establish a dictionary between thermal expectation values of symmetry operators in the Euclidean CFT 𝐷 and the evaluation of gravitational saddles in the presence of a dynamical brane. Expectation values of 0-form symmetry operators in the CFT 𝐷 are then related to branes wrapped on volume minimizing cycles in the bulk, i.e., the Euclidean continuation of a black hole horizon. We illustrate with some representative examples, including gravity in AdS 3 , duality/triality defects in four-dimensional 𝒩 = 4 super Yang-Mills theory, and the dual of R-symmetry operators probing five-dimensional Bogomol’nyi–Prasad–Sommerfield black holes.
T -matrix analysis of static Wilson line correlators from lattice QCD at finite temperature
Here, we utilize a previously constructed thermodynamic T -matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T -matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results.
Further development of finite-temperature density functional theory (Technical Report on FG02-08ER46496)
The final year of funding was spent supporting research into extending conditional probability theory to generate the thermal dependence of PBE. The necessary background work led to a paper being published on the uniform electron gas (Dennis Perchak, Ryan J. McCarty, and Kieron Burke, Phys. Rev. B 105, 165143 (2022).). The graduate student John Kozlowski also contributed to a mathematical paper about DFT (Steven Crisostomo, Ryan Pederson, John Kozlowski, Bhupalee Kalita, Antonio C. Cancio, Kiril Datchev, Adam Wasserman, Suhwan Song, and Kieron Burke, Letters in Mathematical Physics 113, 42 (2023).).