arXiv subjects

Michael Hermele

Publications and source records attributed to Michael Hermele.

64 records · Page 4Linked to original sources

arXiv2008

Properties of an algebraic spin liquid on the kagome lattice

In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the S = 1/2 kagome lattice Heisenberg antiferromagnet. This state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite (ZnCu3(OH)6Cl2). Here, we study the properties of this ASL in more detail, using both the low-energy effective field theory and Gutzwiller-projected wavefunctions. We identify the competing orders of the ASL -- among them we find a set of magnetic orders lying at the M-points of the Brillouin zone, the q = 0 magnetic ordered state, the "Hastings" valence-bond solid (VBS) state, and a pattern of vector spin chirality ordering corresponding to one of the Dzyaloshinskii-Moriya (DM) interaction terms present in herbertsmithite. We discuss the detection of the magnetic and VBS competing orders in experiments. While we focus on a clean system without DM interaction, we consider the effects of small DM interaction and argue that, surprisingly, it leads to spontaneously broken time reversal symmetry (for DM interaction that preserves XY spin rotation symmetry, there is also XY magnetic order). Our analysis of the projected wavefunction provides an estimate of the "Fermi velocity" that characterizes all low-energy excitations of the ASL -- this allows us to estimate the specific heat, which compares favorably with experiments. We also study the spin and bond correlations of the projected wavefunction and compare these results with those of the effective field theory. While the spin correlations in the effective field theory and wavefunction seem to match rather well (although not completely), the bond correlations are more puzzling. We conclude with a discussion of experiments in herbertsmithite and make several predictions.

cond-mat.str-el↗

arXiv2007

Erratum: algebraic spin liquid as the mother of many competing orders

We correct an error in our paper Phys. Rev. B 72, 104404 (2005) [cond-mat/0502215]. We show that a particular fermion bilinear is not related to the other ``competing orders'' of the algebraic spin liquid, and does not possess their slowly decaying correlations. For the square lattice staggered flux spin liquid (equivalently, d-wave RVB state), this observable corresponds to the uniform spin chirality.

cond-mat.str-el↗

arXiv2007

SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice

Motivated by recent experiments on the triangular lattice Mott-Hubbard system kappa-(BEDT-TTF)2Cu2(CN)3, we develop a general formalism to investigate quantum spin liquid insulators adjacent to the Mott transition in Hubbard models. This formalism, dubbed the SU(2) slave-rotor formulation, is an extension of the SU(2) gauge theory of the Heisenberg model to the case of the Hubbard model. Furthermore, we propose the honeycomb lattice Hubbard model (at half-filling) as a candidate for a spin liquid ground state near the Mott transition; this is an appealing possibility, as this model can be studied via quantum Monte Carlo simulation without a sign problem. The pseudospin symmetry of Hubbard models on bipartite lattices turns out to play a crucial role in our analysis, and we develop our formalism primarily for the case of a bipartite lattice. We also sketch its development for a general Hubbard model. We develop a mean-field theory and apply it to the honeycomb lattice. On the insulating side of the Mott transition, we find an SU(2) algebraic spin liquid (ASL), described by gapless S = 1/2 Dirac fermions (spinons) coupled to a fluctuating SU(2) gauge field. We construct a low-energy effective theory describing the ASL phase, the conducting semimetal phase and the Mott transition between them. This physics can be detected in numerical simulations via the simultaneous presence of substantial antiferromagnetic and valence-bond solid correlations. Our analysis suggests that both a third-neighbor electron hopping, and/or pseudospin-breaking terms such as a nearest-neighbor density interaction, may help to stabilize a spin liquid phase.

cond-mat.str-el↗

arXiv2006

Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice

We perform a Gutzwiller projected wavefunction study for the spin-1/2 Heisenberg model on the Kagome lattice to compare energies of several spin-liquid states. The result indicates that a U(1)-Dirac spin-liquid state has the lowest energy. Furthermore, even without variational parameters, the energy turns out to be very close to that found by exact diagonalization. We show that such a U(1)-Dirac state represents a quantum phase whose low energy physics is governed by four flavors of two-component Dirac fermions coupled to a U(1) gauge field. These results are discussed in the context of recent experiments on ZnCu$_3$(OH)$_6$Cl$_2$.

cond-mat.str-el↗

arXiv2005

Universal point contact resistance between thin-film superconductors

A system comprising two superconducting thin films connected by a point contact is considered. The contact resistance is calculated as a function of temperature and film geometry, and is found to vanish rapidly with temperature, according to a universal, nearly activated form, becoming strictly zero only at zero temperature. At the lowest temperatures, the activation barrier is set primarily by the superfluid stiffness in the films, and displays only a weak (i.e., logarithmic) temperature dependence. The Josephson effect is thus destroyed, albeit only weakly, as a consequence of the power-law-correlated superconducting fluctuations present in the films below the Berezinskii-Kosterlitz-Thouless transition temperature. The behavior of the resistance is discussed, both in various limiting regimes and as it crosses over between these regimes. Details are presented of a minimal model of the films and the contact, and of the calculation of the resistance. A formulation in terms of quantum phase-slip events is employed, which is natural and effective in the limit of a good contact. However, it is also shown to be effective even when the contact is poor and is, indeed, indispensable, as the system always behaves as if it were in the good-contact limit at low enough temperature. A simple mechanical analogy is introduced to provide some heuristic understanding of the nearly-activated temperature dependence of the resistance. Prospects for experimental tests of the predicted behavior are discussed, and numerical estimates relevant to anticipated experimental settings are provided.

cond-mat.supr-con↗

arXiv2005

Fate of the Josephson effect in thin-film superconductors

The dc Josephson effect refers to the dissipationless electrical current -- the supercurrent -- that can be sustained across a weak link connecting two bulk superconductors. This effect is a probe of the fundamental nature of the superconducting state. Here, we analyze the case of two superconducting thin films connected by a point contact. Remarkably, the Josephson effect is absent at nonzero temperature, and the resistance across the contact is nonzero. Moreover, the point contact resistance is found to vary with temperature in a nearly activated fashion, with a UNIVERSAL energy barrier determined only by the superfluid stiffness characterizing the films, an angle characterizing the geometry, and whether or not the Coulomb interaction between Cooper pairs is screened. This behavior reflects the subtle nature of the superconductivity in two-dimensional thin films, and should be testable in detail by future experiments.

cond-mat.supr-con↗

arXiv2005

Algebraic spin liquid as the mother of many competing orders

We study the properties of a class of two-dimensional interacting critical states -- dubbed algebraic spin liquids -- that can arise in two-dimensional quantum magnets. A particular example that we focus on is the staggered flux spin liquid, which plays a key role in some theories of underdoped cuprate superconductors. We show that the low-energy theory of such states has much higher symmetry than the underlying microscopic spin system. This symmetry has remarkable consequences, leading in particular to the unification of a number of seemingly unrelated competing orders. The correlations of these orders -- including, in the staggered flux state, the Neel vector and the order parameter for the columnar and box valence-bond solid states -- all exhibit the SAME slow power-law decay. Implications for experiments in the pseudogap regime of the cuprates and for numerical calculations on model systems are discussed.

cond-mat.str-el↗

arXiv2005

Criticality in quantum triangular antiferromagnets via fermionized vortices

We revisit two-dimensional frustrated quantum magnetism from a new perspective, with the aim of exploring new critical points and critical phases. We study easy-plane triangular antiferromagnets using a dual vortex approach, fermionizing the vortices with a Chern-Simons field. Herein we develop this technique for integer-spin systems which generically exhibit a simple paramagnetic phase as well as magnetically-ordered phases with coplanar and collinear spin order. Within the fermionized-vortex approach, we derive a low-energy effective theory containing Dirac fermions with two flavors minimally coupled to a U(1) and a Chern-Simons gauge field. At criticality we argue that the Chern-Simons gauge field can be subsumed into the U(1) gauge field, and up to irrelevant interactions one arrives at quantum electrodynamics in (2+1) dimensions (QED3). Moreover, we conjecture that critical QED3 with full SU(2) flavor symmetry describes the O(4) multicritical point of the spin model where the paramagnet and two magnetically-ordered phases merge. The remarkable implication is that QED3 with flavor SU(2) symmetry is dual to ordinary critical Phi^4 field theory with O(4) symmetry. This leads to a number of unexpected, verifiable predictions for QED3. A connection of our fermionized-vortex approach with the dipole interpretation of the nu=1/2 fractional quantum Hall state is also demonstrated. The approach introduced in this paper will be applied to spin-1/2 systems in a forthcoming publication.

cond-mat.str-el↗

arXiv2004

On the stability of U(1) spin liquids in two dimensions

We establish that spin liquids described in terms of gapless fermionic (Dirac) spinons and gapless U(1) gauge fluctuations can be stable in two dimensions, at least when the physical SU(2) spin symmetry is generalized to SU(N). Equivalently, we show that compact QED3 has a deconfined phase for a large number of fermion fields, in the sense that monopole fluctuations can be irrelevant at low energies. A precise characterization is provided by an emergent global topological U(1) symmetry corresponding to the conservation of gauge flux. Beginning with an SU(N) generalization of the S=1/2 square lattice Heisenberg antiferromagnet, we consider the pi-flux spin liquid and, via a systematic analysis of all operators, show that there are NO relevant perturbations (in the renormalization group sense) about the large-N spin liquid fixed point, which is thus a stable phase. We provide a further illustration of this conclusion with an approximate renormalization group calculation that treats the gapless fermions and the monopoles on an equal footing. This approach directly points out some of the flaws in the erroneous "screening" argument for the relevance of monopoles in compact QED3.

cond-mat.str-el↗

arXiv2003

Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet

We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.

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