In 1935, as part of a broader debate about the interpretation of quantum mechanics, Schrödinger introduced the term “verschränkung” (entanglement) to describe the way in which mutually-exclusive experimental outcomes could be woven together in a single quantum mechanical state. Ninety years later, entanglement is no longer a philosophical curiosity but a technological resource, central to the pursuit of quantum advantage sought in the entanglement of a few hundred qubits. In the context of condensed matter physics, the most celebrated example of entanglement arises in quantum spin liquids (QSL), exotic magnetic phases where, at comparable temperatures, billions of spins can be entangled. The sharpest distinctions between conventional magnetic phases, QSL, and states driven by disorder, are expected to be found in their entanglement properties. Yet exactly what these distinctions are, or how they might be used in experiments, remains poorly understood. In this thesis, we explore how material-based imperfections such as bond disorder and finite temperature affect experimentally accessible entanglement-based diagnostics in models of quantum spin liquids (QSLs). We ask: (1) Can spin liquid states be reliably distinguished from disorder-driven phases using such diagnostics? (2) What can these experimentally accessible entanglement witnesses reveal about the microscopic structure of entanglement in QSLs? In particular, we examine the robustness of these quantum correlations under realistic conditions where thermal fluctuations are unavoidable. In addressing (1), we find that measures like concurrence become unreliable in disordered systems. In contrast, the finite temperature scaling of multipartite diagnostics such as the quantum Fisher information (QFI) provides a more effective means of distinguishing QSLs from competing disorder-dominated phases. For (2), we investigate how the finite temperature behavior of multipartite entanglement measures obtained from semidefinite programming (SDP) methods supports a two step picture for how a high temperature paramagnet crosses over into a QSL ground state. In particular, these results provide a conceptual framework that places quantitative bounds on the temperature window over which candidate materials can be expected to exhibit the characteristic physics of the QSL ground state.
In 1935, as part of a broader debate about the interpretation of quantum mechanics, Schrödinger introduced the term “verschränkung” (entanglement) to describe the way in which mutually-exclusive experimental outcomes could be woven together in a single quantum mechanical state. Ninety years later, entanglement is no longer a philosophical curiosity but a technological resource, central to the pursuit of quantum advantage sought in the entanglement of a few hundred qubits. In the context of condensed matter physics, the most celebrated example of entanglement arises in quantum spin liquids (QSL), exotic magnetic phases where, at comparable temperatures, billions of spins can be entangled. The sharpest distinctions between conventional magnetic phases, QSL, and states driven by disorder, are expected to be found in their entanglement properties. Yet exactly what these distinctions are, or how they might be used in experiments, remains poorly understood. In this thesis, we explore how material-based imperfections such as bond disorder and finite temperature affect experimentally accessible entanglement-based diagnostics in models of quantum spin liquids (QSLs). We ask: (1) Can spin liquid states be reliably distinguished from disorder-driven phases using such diagnostics? (2) What can these experimentally accessible entanglement witnesses reveal about the microscopic structure of entanglement in QSLs? In particular, we examine the robustness of these quantum correlations under realistic conditions where thermal fluctuations are unavoidable. In addressing (1), we find that measures like concurrence become unreliable in disordered systems. In contrast, the finite temperature scaling of multipartite diagnostics such as the quantum Fisher information (QFI) provides a more effective means of distinguishing QSLs from competing disorder-dominated phases. For (2), we investigate how the finite temperature behavior of multipartite entanglement measures obtained from semidefinite programming (SDP) methods supports a two step picture for how a high temperature paramagnet crosses over into a QSL ground state. In particular, these results provide a conceptual framework that places quantitative bounds on the temperature window over which candidate materials can be expected to exhibit the characteristic physics of the QSL ground state.
There are no clean samples in nature. Therefore, when we come to discuss the entanglement properties of quantum materials, the effects of disorder must be taken into account. This question is of particular interest for highly entangled phases, such as quantum spin liquids, which lie outside the Landau paradigm for classifying phases of matter. In this work, we explore what experimentally accessible measures, in the form of concurrence, residual tangle, and quantum Fisher information can teach us about the entanglement in the presence of disorder. As a representative example, we consider the Tomonaga-Luttinger liquids (TLL) and disorder-driven random singlet (RS) phases found in antiferromagnetic quantum spin chains. Using quantum Fisher information and residual tangle, we demonstrate that both TLL and RS phases exhibit multipartite entanglement. In the case of the RS phase, we attribute this to entanglement localized below a crossover length scale. We further show that the order of disorder average matters in calculating measures like concurrence and that this can lead to false inferences when interpreting experiments. Nonetheless, correctly interpreted, these witnesses provide useful information about the effects of disorder. We explore how information about the central charge of the TLL can be extracted from the low-temperature behavior of concurrence and conjecture that this analysis can be extended to the effective central charge of the RS phase. Finally, we establish how RS and TLL phases can be distinguished through the growth of multipartite entanglement, as witnessed by the equal-time structure factor. These results establish that, used carefully, experiments based on entanglement witnesses can provide important information about quantum spin systems in the presence of disorder.
Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.
At the theoretical level, quantum spin liquids are distinguished from other phases of matter by their entanglement properties. However, since the usual measure of entanglement, entanglement entropy, cannot accessed in experiment, indentifying quantum spin liquids in candidate materials remains an acute problem. Here we show other, experimentally-accessible, measures of entanglement can be used to distinguish a quantum spin liquid from a competing disorder-driven "random singlet" phase, in a model of a disordered antiferromagnet on a triangular lattice. The application of these results to the triangular-lattice systems YbZnGaO4, YbZn2GaO5 and KYbSe2 is discussed.
Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.
Quantum Spin Liquids
Quantum spin liquids (QSLs) possess magnetic interactions that, even at absolute zero temperature, remain in a disordered liquid-like spin state. It is very difficult to prove unambiguously that a material is a QSL, because there is always a possibility that it can become ordered below the lowest measured temperature. Barkeshli et al. used quantum field theory to propose a direct way to identify a QSL by placing it in contact with other exotic materials, such as superconductors or magnets. The theory predicted that, at such a boundary, electrons entering the QSL would turn into excitations lacking charge or lacking spin. Future experiments may be able to detect this transmutation.
Science , this issue p. [722][1]
[1]: /lookup/doi/10.1126/science.1253251
This thesis investigates the plausibility of producing a quantum spin liquid (QSL) with ultracold bosonic atoms optically confined to the Mott insulating state. QSLs have received a great deal of attention for being an antiferromagnetic groundstate with many exotic properties, including the absence of local order, long-range entanglement, and fractionalized excitations. However, the identification and characterization of these phases in solid state systems remains a great challenge. Here we outline an alternate route to uncovering the QSL phase, which from the nature of spin angular momentum for ultracold atoms encounters many properties unique to these systems along the way. This proposal is possible because the magnetic exchange interactions for Mott insulating ultracold atoms are mediated by the hopping of whole atoms. Whole-atom exchange—a unique property of cold atoms—allows large fluctuations between the quantized Zeeman sublevels of each atomic spin. As we demonstrate, these fluctuations increase when large-spin atoms are used, or when interactions are tuned via optical Feshbach resonance (OFR). These strong quantum spin fluctuations inhibit classical magnetic ordering, and lead to a QSL ground state. To illustrate the relationship between the spin magnitude, interaction strength, and QSL ground state, we present two distinct approaches to solving the relevant Hamiltonian. With mean field theory we find that for large spin (f > 2), and strong scattering through the spin-singlet channel, that magnetically-ordered Bose-Einstein condensates are unstable to the formation of a QSL. We then utilize Rayleigh-Schodinger perturbation theory to derive an effective Hamiltonian for our system in the Hilbert space of nearest-neighbor singlet coverings. At large spin this Hamiltonian produces a type of quantum dimer model (QDM), which are known to possess QSL phases. We derive the QDM parameters t, t′ and V as a function of spin on several lattices, finding they scale with the inverse number of Zeeman sublevels. We then determine the proximity of the physically accessible states to the QSL phase, and discuss how other regions of the phase diagram may be accessed. We then conclude by highlighting several advantages to studying QSLs and QDMs with ultracold bosons.