Publications by Paul Fendley


Free fermions in disguise

Journal of Physics A: Mathematical and Theoretical IOP Science (2019)

P Fendley

I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local fermions. This construction yields the complete spectrum of the Hamiltonian and an associated classical transfer matrix. The spatially uniform system is gapless with dynamical critical exponent z=3/2, while staggering the couplings gives a more conventional free-fermion model with an Ising transition. The Hamiltonian is equivalent to that of a spin-1/2 chain with next-nearest-neighbour interactions, and has a supersymmetry generated by a sum of fermion trilinears. The supercharges are part of a large non-abelian symmetry algebra that results in exponentially large degeneracies. The model is integrable for either open or periodic boundary conditions but the free-fermion construction only works for the former, while for the latter the extended symmetry is broken and the degeneracies split.


Onsager symmetries in $U(1)$ -invariant clock models

Journal of Statistical Mechanics: Theory and Experiment IOP Science (2019)

E Vernier, E O'Brien, P Fendley

We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a symmetry. We describe in detail the example of nearest-neighbour n-state clock chains whose symmetry is enhanced to . As a consequence of the Onsager-algebra symmetry, the spectrum of these models possesses degeneracies with multiplicities 2 N for positive integer N. We construct the elements of the algebra explicitly from transfer matrices built from non-fundamental representations of the quantum-group algebra . We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. We also find a family of commuting chiral Hamiltonians that break the degeneracies and allow an integrable interpolation between ferro- and antiferromagnets.


John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday Preface

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 51 (2018) ARTN 280301

P Calabrese, P Fendley, U Tauber


Lattice supersymmetry and order-disorder coexistence in the tricritical Ising model

Physical Review Letters American Physical Society 120 (2018) 206403

E O'Brien, P Fendley

We introduce and analyze a quantum spin or Majorana chain with a tricritical Ising point separating a critical phase from a gapped phase with order-disorder coexistence. We show that supersymmetry is not only an emergent property of the scaling limit but also manifests itself on the lattice. Namely, we find explicit lattice expressions for the supersymmetry generators and currents. Writing the Hamiltonian in terms of these generators allows us to find the ground states exactly at a frustration-free coupling. These confirm the coexistence between two (topologically) ordered ground states and a disordered one in the gapped phase. Deforming the model by including explicit chiral symmetry breaking, we find the phases persist up to an unusual chiral phase transition where the supersymmetry becomes exact even on the lattice.


Condensation-driven phase transitions in perturbed string nets

Physical Review B 96 (2017)

M Mariën, J Haegeman, P Fendley, F Verstraete


Long coherence times for edge spins

Journal of Statistical Mechanics: Theory and Experiment 2017 (2017) 063105-063105

J Kemp, NY Yao, CR Laumann, P Fendley


Prethermal strong zero modes and topological qubits

Physical Review X American Physical Society 7 (2017) 041062

DV Else, P Fendley, J Kemp, C Nayak

We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures, the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This nonequilibrium dynamical phenomenon is a form of prethermalization and occurs because of obstructions to the equilibration of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a nonperturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes and on trapped ion chains.


Deconfinement transitions in a generalised XY model

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 50 (2017) ARTN 424003

P Serna, JT Chalker, P Fendley


Strong zero modes and eigenstate phase transitions in the XYZ/interacting Majorana chain

Journal of Physics A: Mathematical and Theoretical 49 (2016) 30LT01-30LT01

P Fendley


Topological defects on the lattice: I. The Ising model

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 49 (2016) ARTN 354001

D Aasen, RSK Mong, P Fendley


Topological phases with parafermions: theory and blueprints

Annual Review of Condensed Matter Physics Annual Reviews 7 (2016) 119-139

J Alicea, P Fendley

We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.


Geometric mutual information at classical critical points.

Physical review letters 112 (2014) 127204-

J-M Stéphan, S Inglis, P Fendley, RG Melko

A practical use of the entanglement entropy in a 1D quantum system is to identify the conformal field theory describing its critical behavior. It is exactly (c/3)lnℓ for an interval of length ℓ in an infinite system, where c is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2D conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to c. This makes it possible to extract c in classical simulations, which we demonstrate for the critical Ising and three-state Potts models.


Parafermionic conformal field theory on the lattice

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 47 (2014) ARTN 452001

RSK Mong, DJ Clarke, J Alicea, NH Lindner, P Fendley


Stability of zero modes in parafermion chains

PHYSICAL REVIEW B 90 (2014) ARTN 165106

AS Jermyn, RSK Mong, J Alicea, P Fendley


Corner contribution to the entanglement entropy of an O(3) quantum critical point in 2+1 dimensions

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2014) ARTN P06009

AB Kallin, EM Stoudenmire, P Fendley, RRP Singh, RG Melko


Universal Topological Quantum Computation from a Superconductor-Abelian Quantum Hall Heterostructure

PHYSICAL REVIEW X 4 (2014) ARTN 011036

RSK Mong, DJ Clarke, J Alicea, NH Lindner, P Fendley, C Nayak, Y Oreg, A Stern, E Berg, K Shtengel, MPA Fisher


Free parafermions

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 47 (2014) ARTN 075001

P Fendley


Exactly solvable lattice models with crossing symmetry

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 46 (2013) ARTN 105002

SH Simon, P Fendley


Fibonacci topological order from quantum nets.

Physical review letters 110 (2013) 260408-

P Fendley, SV Isakov, M Troyer

We analyze a model of quantum nets and show it has a non-Abelian topological order of doubled-Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins around a face, around a vertex, and special "Jones-Wenzl" terms that serve to couple long loops together. We provide strong evidence for a gap by exact diagonalization, completing the list of ingredients necessary for topological order.


Entanglement in gapless resonating-valence-bond states

NEW JOURNAL OF PHYSICS 15 (2013) ARTN 015004

J-M Stephan, H Ju, P Fendley, RG Melko

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