Pseudo-fermion functional renormalization group for spin models

Reports on Progress in Physics, Journal Year: 2024, Volume and Issue: 87(3), P. 036501 - 036501

Published: Jan. 19, 2024

Abstract For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools low-dimensional magnetism thrived improved recent years due to breakthroughs inspired by information computation, higher-dimensional can be considered final frontier, where strong entanglement, multiple ordering channels, manifold ways of paramagnetism culminate. At same time, efforts crystal synthesis induced significant increase number tangible which are generically three-dimensional nature, creating an urgent need quantitative theoretical modeling. We review pseudo-fermion (PF) pseudo-Majorana (PM) functional renormalization group (FRG) their specific ability address magnetism. First developed more than decade ago, PFFRG interprets Heisenberg model Hamiltonian terms Abrikosov pseudofermions, is then treated diagrammatic resummation scheme formulated flow m -particle pseudofermion vertices. The article reviews state art PMFRG discusses application exemplary domains magnetism, but most importantly, it makes algorithmic implementation details these methods accessible everyone. By thus lowering entry barrier application, we hope that this will contribute towards establishing addressing higher spatial dimensions.

Language: Английский

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Pseudo-Majorana functional renormalization for frustrated XXZ spin- 12 models with field or magnetization along the spin- Z direction at finite temperature

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(5)

Published: Feb. 13, 2025

The numerical study of high-dimensional frustrated quantum magnets remains a challenging problem. Here we present an extension the pseudo-Majorana functional renormalization group to spin-1/2 XXZ-type Hamiltonians with field or magnetization along spin-Z direction at finite temperature. We consider U(1) symmetry-adapted fermionic spin representation and derive diagrammatic framework its flow equations. discuss benchmark results application two antiferromagnetic triangular lattice materials recently studied in experiments applied magnetic fields: First, numerically reproduce data measured for CeMgAl11O19 confirming model parameters previously estimated from inelastic neutron spectrum high fields. Second, showcase accuracy our method by studying thermal phase transition into solid up-up-down Na2BaCo(PO4)2 good agreement experiment. Published American Physical Society 2025

Language: Английский

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Renormalized Classical Spin Liquid on the Ruby Lattice

Physical Review Letters, Journal Year: 2025, Volume and Issue: 134(8)

Published: Feb. 27, 2025

The recent experimental detection of the onset a dynamically prepared, gapped Z2 quantum spin liquid on ruby lattice brought physics frustrated magnetism and gauge theory to Rydberg tweezer arrays [Semeghini , Probing topological liquids programmable simulator, ]. thermodynamic properties such models remain inadequately addressed, yet knowledge thereof is indispensable if one wants prepare large, robust, long-lived liquids. Using large scale Monte Carlo simulations we find in model renormalized classical with constant entropy density S/N approaching ln(2)/6 limit for all moderate values detuning δ starting from T/Ω∼0.5 (in units Rabi frequency Ω) down lowest temperatures could simulate, T/Ω∼0.01. With van der Waals interactions, plateaus are still found but its value shifts δ. We comment implications adiabatic approximation dynamical ramps electric degrees freedom, which leads reinterpretation observations. Published by American Physical Society 2025

Language: Английский

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Supersolidity in Rydberg tweezer arrays

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(1)

Published: Jan. 31, 2025

Rydberg tweezer arrays provide a versatile platform to explore quantum magnets with dipolar XY or van der Waals Ising ZZ interactions. Here, we propose scheme combining and interactions between two states, where the amplitude of latter can be greater than that former, realizing an extended Hubbard model long-range tunnelings in optical arrays. On triangular lattice repulsive interactions, predict existence robust supersolid phase critical entropy per particle S/N≈0.19 accessible current experiments supported by large-scale Monte Carlo simulations. We further demonstrate experimental feasibility identifying pairs states Rb87 required Such is long lived, found over wide parameter range isotropic flat two-dimensional geometry, realized for hundreds particles allowing one directly probe defect-induced picture supersolids. Its thermodynamical dynamical properties hence studied at far larger scale hitherto possible. Published American Physical Society 2025

Language: Английский

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Temperature flow in pseudo-Majorana functional renormalization for quantum spins

Physical review. B./Physical review. B, Journal Year: 2024, Volume and Issue: 109(19)

Published: May 3, 2024

We implement the temperature flow scheme first proposed by Honerkamp and Salmhofer [Phys. Rev. B 64, 184516 (2001)] into pseudo-Majorana functional renormalization group method for quantum spin systems. Since parameter in this approach is a physical quantity, $T$, numerical efficiency increases significantly compared to more conventional parameters, especially when computing finite-temperature phase diagrams. apply determine diagram of ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on simple cubic lattice, where our findings support claims vanishingly small nonmagnetic around high frustration point ${J}_{2}=0.25{J}_{1}$. Perhaps most importantly, we find be advantageous detecting transitions as, construction, transition never encountered at an artificial, unphysical cutoff parameter. Finally, dipolar XXZ square rich with large regime down lowest accessible temperatures. Wherever comparison error-controlled (quantum) Monte Carlo methods applicable, excellent quantitative agreement less than $5%$ deviation from numerically exact results.

Language: Английский

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Scale-invariant phase transition of disordered bosons in one dimension

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(2)

Published: Jan. 8, 2025

Language: Английский

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All product eigenstates in Heisenberg models from a graphical construction

Physical Review Research, Journal Year: 2025, Volume and Issue: 7(1)

Published: Jan. 10, 2025

Recently, large degeneracy based on product eigenstates has been found in spin ladders, kagome-like lattices, and motif magnetism, connected to liquids, anyonic phases, quantum scars. We unify these systems by a complete classification of Heisenberg XXZ Hamiltonians with Dzyaloshinskii-Moriya interaction general graphs the form Kirchhoff rules for supercurrents. By this, we construct extensive degree linked exotic condensates which could be studied atomic gases lattices. Published American Physical Society 2025

Language: Английский

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Continuously varying critical exponents in an exactly solvable long-range cluster XY model

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(2)

Published: Feb. 6, 2025

We investigate a generalized antiferromagnetic cluster XY model in transverse magnetic field, where long-range interactions decay algebraically with distance. This can be exactly solvable within free fermion framework. By analyzing the gap, we explicitly derive critical exponents $\nu$ and $z$, finding that relationship $\nu z = 1$ still holds. However, values of $z$ depend on decaying exponent $\alpha$, contrast to those for quantum Ising chain. To optimize scaling behavior, verify these using correlation functions fidelity susceptibility, achieving excellent data collapse across various system sizes by adjusting fitting parameters. Finally, compute entanglement entropy at point determine central charge $c$, find it also varies $\alpha$. study provides insights into unique effect properties spin systems.

Language: Английский

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Helicity modulus in the bilayer XY model by the Monte Carlo worm algorithm

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(9)

Published: March 11, 2025

Language: Английский

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Phase diagram of the XXZ pyrochlore model from pseudo-Majorana functional renormalization group

Physical review. B./Physical review. B, Journal Year: 2025, Volume and Issue: 111(13)

Published: April 24, 2025

We calculate the magnetic phase diagram of spin-1/2 nearest neighbor XXZ pyrochlore model using pseudo-Majorana functional renormalization group in temperature flow formalism. Our as a function and coupling ratio, allowing both longitudinal transverse couplings to be ferromagnetic antiferromagnetic, reveals large nonmagnetic regime at low temperatures, which includes quantum spin ice near antiferromagnetic Ising model, well Heisenberg XY models. are able detect transitions via critical finite size scaling down temperatures two orders magnitude smaller than interactions, demonstrating remarkably good performance our method upon approaching ground state. Specifically, low-temperature transition from zero-flux into shows very agreement with previous Monte Carlo results. Comparing findings classical results, we identify order-by-disorder effect model. In magnetically disordered regimes, find characteristic patterns broadened pinch points structure factor investigate their evolution when ordered phases. also compute linear responses lattice symmetry breaking perturbations possible nematic state Published by American Physical Society 2025

Language: Английский

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