The Hubbard Model

Annual Review of Condensed Matter Physics, Journal Year: 2021, Volume and Issue: 13(1), P. 239 - 274

Published: Nov. 19, 2021

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic of field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent that observed quantum materials. Nevertheless, much phase diagram remains controversial. Here, we review subset what known about model, based on exact results or controlled approximate solutions various limits, for there suitable small parameter. Our primary focus ground state properties system lattices two spatial dimensions, although both lower higher dimensions are discussed well. Finally, highlight some important outstanding open questions.

Language: Английский

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The Hubbard Model: A Computational Perspective

Annual Review of Condensed Matter Physics, Journal Year: 2021, Volume and Issue: 13(1), P. 275 - 302

Published: Nov. 29, 2021

The Hubbard model is the simplest of interacting fermions on a lattice and similar importance to correlated electron physics as Ising statistical mechanics or fruit fly biomedical science. Despite its simplicity, exhibits an incredible wealth phases, phase transitions, exotic correlation phenomena. While analytical methods have provided qualitative description in certain limits, numerical tools shown impressive progress achieving quantitative accurate results over last years. This article gives introduction model, motivates common questions, illustrates that has been achieved years revealing various aspects model.

Language: Английский

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Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids

Reviews of Modern Physics, Journal Year: 2022, Volume and Issue: 94(3)

Published: Sept. 14, 2022

The Sachdev-Ye-Kitaev (SYK) model is a solvable of many-body quantum system that has stimulated interest in both condensed matter physics and gravity. This review focuses on the insights provided by SYK model, which no quasiparticle excitations, into Planckian non-Fermi-liquid metals. discussed for range strongly correlated models relation to experiments materials. Also included discussion recent developments regarding connections between theory black holes.

Language: Английский

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Colloquium : Planckian dissipation in metals

Reviews of Modern Physics, Journal Year: 2022, Volume and Issue: 94(4)

Published: Nov. 30, 2022

We review the appearance of Planckian time $\tau_\text{Pl} = \hbar/(k_B T)$ in both conventional and unconventional metals. give a pedagogical discussion various different timescales (quasiparticle, transport, many-body) that characterize metals, emphasizing conditions under which these times are same or different. Throughout, we have attempted to clear up aspects problem had been confusing us, hope this helps reader as well. discuss possibility bound on dissipation from quasiparticle many-body perspective. quasiparticles can arise naturally combination inelastic scattering mass renormalization. Many-body dynamics, other hand, is constrained by basic time- length- scales local thermalization.

Language: Английский

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Stranger than metals

Science, Journal Year: 2022, Volume and Issue: 377(6602)

Published: July 7, 2022

Although the resistivity in traditional metals increases with temperature, its $T$ dependence vanishes at low or high albeit for different reasons. Here, we review a class of materials, known as \lq strange' metals, that can violate both principles. In materials exhibiting such behavior, change slope mean free path drops below lattice constant, $T \rightarrow 0$, be imperceptible, suggesting complete continuity between charge carriers and $T$. Since particles cannot scatter length scales shorter than interatomic spacing, strange metallicity calls into question relevance locality particle picture underlying current. This focuses on transport spectroscopic data candidate an eye to isolate identify unifying physical principle. Special attention is paid quantum criticality, Planckian dissipation, Mottness, whether new gauge principle, which has clear experimental signature, needed account non-local seen metals. For cuprates, shown track superfluid density, thereby making theory this state primary hurdle solving riddle high-temperature superconductivity.

Language: Английский

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Quantum critical points and the sign problem

Science, Journal Year: 2022, Volume and Issue: 375(6579), P. 418 - 424

Published: Jan. 27, 2022

The "sign problem" (SP) is the fundamental limitation to simulations of strongly correlated materials in condensed matter physics, solving quantum chromodynamics at finite baryon density, and computational studies nuclear matter. As a result, it part reason fields such as ultra-cold atomic physics are so exciting: they can provide emulators models that could not otherwise be solved, due SP. For same reason, also one primary motivations behind computation. It often argued SP intrinsic particular Hamiltonians, since details how onsets, its eventual occurrence, altered by choice algorithm or many-particle basis. Despite that, we show determinant Monte Carlo (DQMC) quantitatively linked critical behavior. We demonstrate this via number including spinful spinless Hubbard Hamiltonians on honeycomb lattice ionic Hamiltonian, all whose properties relatively well understood. then propose reinterpretation low average sign for model square when away from half-filling, an important open problem terms onset pseudogap behavior exotic superconductivity. Our study charts path exploiting QMC understand behavior, rather than solely obstacle prevents many-body temperature.

Language: Английский

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Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(3)

Published: Jan. 10, 2025

Language: Английский

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Cuprate superconductors as viewed through a striped lens

Advances In Physics, Journal Year: 2020, Volume and Issue: 69(4), P. 437 - 509

Published: Oct. 1, 2020

Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, particular because "normal" state from which it evolves is unprecedented. Now, after three and half decades of research, involving wide range experimental characterizations, possible to delineate clear consistent story. It starts with doping holes into charge-transfer insulator, resulting in-gap states. These states exhibit pseudogap competition between antiferromagnetic superexchange J nearest-neighbor Cu atoms (a real-space interaction) kinetic energy doped holes, which, absence interactions, would lead extended Bloch-wave whose occupancy characterized reciprocal space. To develop some degree coherence on cooling, spin charge correlations must self-organize cooperative fashion. A specific example emergent order that stripes, as observed La2−xBaxCuO4. While stripe frustrates bulk superconductivity, nevertheless develops superconducting an unusual character. The antiphase stripes decouples them can be viewed hole-doped, two-leg, spin-12 ladders. Established theory tells us scale comparable singlet-triplet excitation energy, ∼J/2, achieve order, pair neighboring ladders phase order. In presence Josephson coupling pair-density-wave superconductivity. Alternatively, in-phase superconductivity requires have gap, empirically limits coherent gap. Hence, cuprates involves compromise scale, maximized at x∼18, coherence, optimized x∼0.2. understand further details, necessary take account local variation hole density dopant disorder poor screening long-range Coulomb interactions. At large doping, wins out over J, regions intertwined become sparse, disappears. there are few mysteries remain resolved, I believe this story captures essence cuprates.

Language: Английский

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Enhanced superconductivity by near-neighbor attraction in the doped extended Hubbard model

Physical review. B./Physical review. B, Journal Year: 2023, Volume and Issue: 107(20)

Published: May 3, 2023

Recent experiment has unveiled an anomalously strong electron-electron attraction in one-dimensional copper-oxide chain Ba$_{2-x}$Sr$_x$CuO$_{3+\delta}$. While the near-neighbor electron $V$ extended Hubbard been examined recently, its effect model beyond remains unclear. We report a density-matrix renormalization group study of on long four-leg cylinders square lattice. find that can notably enhance long-distance superconducting correlations while simultaneously suppressing charge-density-wave correlations. Specifically, for modestly attraction, become dominant over CDW with Luttinger exponent $K_{sc}\sim 1$ and divergent susceptibility. Our results provide promising way to realize long-range superconductivity doped two dimensions. The relevance our numerical cuprate materials is also discussed.

Language: Английский

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Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model

Physical Review Letters, Journal Year: 2023, Volume and Issue: 130(22)

Published: June 1, 2023

Accurate simulations of the two-dimensional (2D) Hubbard model constitute one most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for calculations 2D at finite temperature. An optimal evolution density operator is achieved tanTRG with mild O(D3) complexity, where bond dimension D controls accuracy. With boost low-temperature large-scale systems on up to width-8 cylinder 10×10 square lattice. For half-filled model, obtained results are excellent agreement those determinant Monte Carlo (DQMC). Moreover, can be used explore low-temperature, finite-doping regime inaccessible DQMC. The calculated charge compressibility Matsubara Green's function found reflect strange metal pseudogap behaviors, respectively. superconductive pairing susceptibility computed down low temperature approximately 1/24 hopping energy, find d-wave responses significant near doping. Equipped tangent-space technique, constitutes well-controlled, highly efficient accurate network method strongly correlated lattice models temperature.Received 11 January 2023Revised 17 March 2023Accepted 25 April 2023DOI:https://doi.org/10.1103/PhysRevLett.130.226502© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFermi surfaceMagnetismPseudogapSuperconductivityThermodynamicsPhysical SystemsStrongly systemsTechniquesHubbard modelTensor methodsCondensed Matter, Materials & Applied PhysicsNetworksStatistical PhysicsQuantum Information

Language: Английский

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