• physics 17, 63
Numerical studies reveal surprising correspondences between lattice spin models and quantum field theory.
O. Starykh/University of Utah; adapted by APS/Carin Cain
The search for quantum spin liquids (QSLs) in truly magnetic materials has been at the forefront of condensed matter physics since this exotic quantum state was first proposed more than half a century ago. Meanwhile, theorists continue to work to understand the rich physics that might emerge from such a state. Now, Alexander Wietek and his collaborators at the Max Planck Institute for Complex Systems Physics in Germany have made significant progress toward this goal.Through numerical simulations, they made a convincing numerical case that the well-studied fundamental excitation spectrum of QSL has a one-to-one correspondence with the well-studied excitation spectrum of quantum field theory. [1]. If a true QSL is discovered or made, this correspondence would open up the prospect of testing particle physics theories with condensed matter systems. For example, it would provide us with a new “habitat” where hypothetical elementary particles, such as magnetic monopoles, could be discovered.
The word “liquid” in QSL implies the fluid-like behavior of magnetic moments (spins), which form a fundamental component of theoretical models describing magnetic materials. In most QSL models, spins are periodically arranged in a two- or three-dimensional lattice. However, their orientation does not show any obvious periodic pattern, but performs a never-ending quantum mechanical dance for which the only classical analogy might be that of a flowing liquid.
It has long been recognized that for spins to form a liquid, they must interact antiferromagnetically with neighboring spins, that is, the interacting spin pairs should minimize their energy by becoming antiparallel. [2]. At the same time, the lattice in which the spins reside must be frustrated—that is, its geometry should be such that it is impossible for the spins to fall on and point toward a single common axis in spin space.
A two-dimensional triangular lattice can accommodate QSL. However, this seeming simplicity is deceptive. Consider the case where spins on a triangular lattice interact only with their nearest neighbors (an interaction called exchange) J1). A large number of numerical and approximate analytical studies have confirmed that this situation forms an ordered “120° state” (Figure 1).However, adding small antiferromagnetic interactions J2 Next nearest neighbor trick [3].This model is called the Heisenberg model J1 – J2 Triangular antiferromagnet. Several numerical studies have explored this model using different numerical methods.They all found that the ground state is a spin liquid when 0.07 < J2/J1 < 0.15.This novel quantum state is bounded by the 120° state at small J2 and another ordered state, the collinear striped state, in the larger J2.
One of the studies also found that the lowest energy state of the model can be described by Dirac QSL [4]. Wietek and his collaborators explored the rich structure of this state in their new study. The theoretical description of Dirac’s QSL and quantum electrodynamics (QED) in two spatial directions plus time3) and two-dimensional graphene. Like graphene, Dirac QSL possesses two sets of massless Dirac fermions, corresponding to different valleys in the Brillouin zone. In addition, both sets of fermions carry additional internal (sublattice) indexes and spin quantum numbers. Fermions are constrained by the fact that each position of the triangular lattice is occupied by exactly one particle. In momentum space this translates into a filled lower Dirac belt and an empty upper Dirac belt.
Similarities between Dirac QSL and QED3 Previously proposed in the description of field theory J1 – J2 Heisenberg antiferromagnet on Kagome lattice [5]. Here, the occupancy constraints are enforced by the class-time component (scalar potential) of the emerging dynamic gauge field. The emergence of gauge fields is inevitable because each spin operator is “decomposed” into the product of two fermion operators. The spatial component of the gauge field originates from phase fluctuations in the exchange interactions between spins.
Quantum economic development3 The structure of the above-mentioned Dirac QSL implies a variety of possible excitations, the most important of which are particle hole excitations of Dirac fermions, photon-like waves of gauge fields, and magnetic monopoles.These excitations are characterized by quantum numbers such as momentum and spin, as well as lattice space group operations [5, 6]. Wietek and his collaborators constructed all possible QEDs3 Excitations on carefully selected 36-bit clusters are then evaluated for their overlap with numerically accurate low-energy eigenstates of a lattice spin model on the same cluster for the same set of quantum numbers. The results are encouraging. For a total of nearly 200 eigenstates, they found significant overlap in the spin liquid region, ranging from 0.4 to 0.9.This extraordinary discovery establishes an essentially one-to-one correspondence between QED3 and J1 – J2 Heisenberg model.
An analogy to physicist Robert Laughlin’s famous 1983 paper provides a useful perspective on this result [7]which demonstrates the numerical calculation of the ground state and ν = 1/3 Fractional Quantum Hall. This overlap is similar to the newly discovered QSL-QED3 communication, helping to open the door for fractional quasiparticles to become candidates for topological quantum computing.
More work needs to be done to better understand how QED3 Excitation manifests itself in the physical response of frustrated antiferromagnets, which is crucial for the experimental detection of QSL [8].Another important issue concerns the stability of Dirac QSL to physical perturbations, such as the introduction of spin-lattice coupling and the application of external magnetic fields [9]. Progress along these and related directions requires a better analytical and numerical understanding of the correlation functions of physical operators constructed from magnetic monopoles. With more work, a breakthrough could come soon.
refer to
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- PW Anderson, Resonant Valence Bonding: A New Insulator? Matt. resource. bull. 8153 (1973).
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- M. Helmele et al.Properties of algebraic spin liquids on Kagome lattices, physics. Revision B 77224413 (2008).
- X.-Y.song et al.a unified description of competitive order in two-dimensional quantum magnets, Nat. comminicate. 104254 (2019).
- RB Laughlin, The Anomalous Quantum Hall Effect: Incompressible Quantum Fluids with Fractional Charge Excitations, physics. Pastor Wright. 501395 (1983).
- F. Ferrari and F. Becca, dynamic structural coefficients J1 J2 Heisenberg model on triangular lattice: magnons, spinons and gauge fields, physics. Revision X 9031026 (2019); Sherman et al.The spectral function of J1 J2 Heisenberg model on triangular lattice, physics. Revision B 107165146 (2023); M. Drescher et al.symmetry breaking and dynamic characteristics of the liquid phase S = Antiferromagnet on Heisenberg triangle lattice, 108L220401 (2023).
- UFP Seifert et al.Spin-Peierls instability U(1) Dirac spin liquid, arXiv:2307.12295; Ran Yu et al.Spontaneous spin ordering of Dirac spin liquid in magnetic field, physics. Pastor Wright. 102047205 (2009).
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