arXiv subjects

Jiannis K. Pachos

Publications and source records attributed to Jiannis K. Pachos.

At least 37 records · Page 2Linked to original sources

arXiv2023

Emerging (2+1)D massive graviton in graphene-like systems

Unlike the fundamental forces of the Standard Model the quantum effects of gravity are still experimentally inaccessible. Rather surprisingly quantum aspects of gravity, such as massive gravitons, can emerge in experiments with fractional quantum Hall liquids. These liquids are analytically intractable and thus offer limited insight into the mechanism that gives rise to quantum gravity effects. To thoroughly understand this mechanism we employ a graphene-like system and we modify it appropriately in order to realise a simple (2+1)-dimensional massive gravity model. More concretely, we employ (2+1)-dimensional Dirac fermions, emerging in the continuous limit of a fermionic honeycomb lattice, coupled to massive gravitons, simulated by bosonic modes positioned at the links of the lattice. The quantum character of gravity can be determined directly by measuring the correlations on the bosonic atoms or by the interactions they effectively induce on the fermions. The similarity of our approach to current optical lattice configurations suggests that quantum signatures of gravity can be simulated in the laboratory in the near future, thus providing a platform to address question on the unification theories, cosmology or the physics of black holes.

quant-ph↗

arXiv2023

$Q$-Deformed Rainbows: a Universal Simulator of Free Entanglement Spectra

The behaviour of correlations across a bipartition is an indispensable tool in diagnosing quantum phases of matter. Here we present a spin chain with position-dependent XX couplings and magnetic fields, that can reproduce arbitrary structure of free fermion correlations across a bipartition. In particular, by choosing appropriately the strength of the magnetic fields we can obtain any single particle energies of the entanglement spectrum with high fidelity. The resulting ground state can be elegantly formulated in terms of $q$-deformed singlets. To demonstrate the versatility of our method we consider certain examples, such as a system with homogeneous correlations and a system with correlations that follow a prime number decomposition. Hence, our entanglement simulator can be easily employed for the generation of arbitrary entanglement spectra with possible applications in quantum technologies and condensed matter physics.

quant-ph↗

arXiv2023

Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics

The interface between different quantum phases of matter can give rise to novel physics, such as exotic topological phases or non-unitary conformal field theories. Here we investigate the interface between two spin chains in different chiral phases. Surprisingly, the mean-field theory description of this interacting composite system is given in terms of Dirac fermions in a curved space-time geometry. In particular, the boundary between the two phases represents a black hole horizon. We demonstrate that this representation is faithful both analytically, by employing bosonisation to obtain a Luttinger liquid model, and numerically, by employing Matrix Product State methods. A striking prediction from the black hole equivalence emerges when a quench, at one side of the interface between two opposite chiralities, causes the other side to thermalise with the Hawking temperature for a wide range of parameters and initial conditions.

cond-mat.str-el↗

arXiv2022

Break-in' Point: Somatic narratives: The convergence of arts and science in the transformation of temporal communities

Break-in' Point, a 2012 arts and science performance and community engagement research initiative, was presented in the spring and fall semesters at the University of Leeds in the United Kingdom at Stage@Leeds. The outcome of a collaboration between dance artist A3 and theoretical physicist A2, under the direction of performance researcher A1, Break-in' Point is based on a series of real-life encounters at intersections of arts and science - exploring force, risk, exposure and resilience. The Break-in' Point performance offered an interrogation of the critical point at which physical, mental, and/or emotional strength give way under stress - causing structural degeneration and the experience of what lies beyond. This article is an examination of the performance, reviewing and analysing it as an imagined somatic zone - embodied encounters that transcend temporal bound-ness, compelling and igniting new possibilities - that engaged spiritual and epistemological transformation of performers and audiences. The article addresses three main periods in the life of Break-in' Point: (1) the development period - script building and rehearsals, (2) the performance - live encounters between and among performers and audiences and (3) beyond the theatre - digital engagements in the classroom and pedagogy. The article contributes new concepts and new ways of thinking about science education, the role of digital technology in pedagogy, dance/theatre public engagement and community arts practices as practices of healing, health and resilience.

physics.ed-ph↗

arXiv2022

Universality of Z3 parafermions via edge mode interaction and quantum simulation of topological space evolution with Rydberg atoms

Parafermions are Zn generalisations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. We study the simplest case of the Z3 parafermion chain and investigate the form of the non-topological gate that arises through direct short-range interaction of the parafermion edge modes. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, with the strongest order of the interaction generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We also illustrate the accessibility of highly non-contextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z3 topological states with Rydberg atom technology.

quant-ph↗

arXiv2021

Non-Abelian statistics with mixed-boundary punctures on the toric code

The toric code is a simple and exactly solvable example of topological order realising Abelian anyons. However, it was shown to support non-local lattice defects, namely twists, which exhibit non-Abelian anyonic behaviour [1]. Motivated by this result, we investigated the potential of having non-Abelian statistics from puncture defects on the toric code. We demonstrate that an encoding with mixed-boundary punctures reproduces Ising fusion, and a logical Pauli-$X$ upon their braiding. Our construction paves the way for local lattice defects to exhibit non-Abelian properties that can be employed for quantum information tasks.

quant-ph↗

arXiv2021

Edge density of bulk states due to relativity

The boundaries of quantum materials can host a variety of exotic effects such as topologically robust edge states or anyonic quasiparticles. Here, we show that fermionic systems such as graphene that admit a low energy Dirac description can exhibit counterintuitive relativistic effects at their boundaries. As an example, we consider carbon nanotubes and demonstrate that relativistic bulk spinor states can have non zero charge density on the boundaries, in contrast to the sinusoidal distribution of non-relativistic wave functions that are necessarily zero at the boundaries. This unusual property of relativistic spinors is complementary to the linear energy dispersion relation exhibited by Dirac materials and can influence their coupling to leads, transport properties or their response to external fields.

cond-mat.mes-hall↗

arXiv2021

Topological contextuality and anyonic statistics of photonic-encoded parafermions

Quasiparticle poisoning, expected to arise during the measurement of Majorana zero mode state, poses a fundamental problem towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can encode topological qudits immune to quasiparticle poisoning. While parafermions are expected to emerge in superconducting fractional quantum Hall systems, they are not yet attainable with current technology. To bypass this problem, we employ a photonic quantum simulator to experimentally demonstrate the key components of parafermion-based universal quantum computation. Our contributions in this article are twofold. First, by manipulating the photonic states, we realize Clifford operator Berry phases that correspond to braiding statistics of parafermions. Second, we investigate the quantum contextuality in a topological system for the first time by demonstrating the contextuality of parafermion encoded qudit states. Importantly, we find that the topologically-encoded contextuality opens the way to magic state distillation, while both the contextuality and the braiding-induced Clifford gates are resilient against local noise. By introducing contextuality, our photonic quantum simulation provides the first step towards a physically robust methodology for realizing topological quantum computation.

quant-ph↗

arXiv2021

Photonic implementation of Majorana-based Berry phases

Geometric phases, generated by cyclic evolutions of quantum systems, offer an inspiring playground for advancing fundamental physics and technologies, alike. Intriguingly, the exotic statistics of anyons realised in physical systems can be interpreted as a topological version of geometric phases. However, non-Abelian statistics has not yet been demonstrated in the laboratory. Here we employ an all optical quantum system that simulates the statistical evolution of Majorana fermions. As a result we experimentally realise non-Abelian Berry phases with the topological characteristic that they are invariant under continues deformations of their control parameters. We implement a universal set of Majorana inspired gates by performing topological and non-topological evolutions and investigate their resilience against perturbative errors. Our photonic experiment, while it is not scalable, it suggests the intriguing possibility of experimentally simulating Majorana statistics with scalable technologies.

quant-ph↗

arXiv2021

Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation

Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three-dimensional topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2020

Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model

We demonstrate that $\mathbb{Z}_2$ gauge transformations and lattice deformations in Kitaev's honeycomb lattice model can have the same description in the continuum limit of the model in terms of chiral gauge fields. The chiral gauge fields are coupled to the Majorana fermions that satisfy the Dirac dispersion relation in the non-Abelian sector of the model. For particular values, the effective chiral gauge field becomes equivalent to the $\mathbb{Z}_2$ gauge field, enabling us to associate effective fluxes to lattice deformations. Motivated by this equivalence, we consider Majorana-bounding $π$ vortices and Majorana-bounding lattice twists and demonstrate that they are adiabatically connected to each other. This equivalence opens the possibility for novel encoding of Majorana-bounding defects that might be easier to realise in experiments.

cond-mat.str-el↗

arXiv2020

Topological Quantum Liquids with Long-Range Couplings

Very few topological systems with long-range couplings have been considered so far due to our lack of analytic approaches. Here we extend the Kitaev chain, a 1D quantum liquid, to infinite-range couplings and study its topological properties. We demonstrate that, even though topological phases are intimately linked to the notion of locality, the infinite-range couplings give rise to topological zero and non-zero energy Majorana end modes depending on the boundary conditions of the system. We show that the analytically derived properties are to a large degree stable against modifications to decaying long-range couplings. Our work opens new frontiers for topological states of matter that are relevant to current experiments where suitable interactions can be designed.

cond-mat.str-el↗

arXiv2020

Geometric description of the Kitaev honeycomb lattice model

It is widely accepted that topological superconductors can only have an effective interpretation in terms of curved geometry rather than gauge fields due to their charge neutrality. This approach is commonly employed in order to investigate their properties, such as the behaviour of their energy currents. Nevertheless, it is not known how accurately curved geometry can describe actual microscopic models. Here, we demonstrate that the low-energy properties of the Kitaev honeycomb lattice model, a topological superconductor that supports localised Majorana zero modes at its vortex excitations, are faithfully described in terms of Riemann-Cartan geometry. In particular, we show analytically that the continuum limit of the model is given in terms of the Majorana version of the Dirac Hamiltonian coupled to both curvature and torsion. We numerically establish the accuracy of the geometric description for a wide variety of couplings of the microscopic model. Our work opens up the opportunity to accurately predict dynamical properties of the Kitaev model from its effective geometric description.

cond-mat.str-el↗

arXiv2020

Topological bulk states and their currents

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients are applied to the bulk, while all parts of the system remain adiabatically connected to the same phase. In turn, the bulk states produce bulk current transverse to the strain. This occurs even when the potential is always below the energy gap, where one expects only edge currents to appear. Bulk currents are topologically protected and behave like edge currents under external influence, such as temperature or local disorder. Detecting topologically resilient bulk currents offers a direct means to probe the localised bulk states.

cond-mat.mes-hall↗

arXiv2020

Specific heat of 2D interacting Majorana fermions from holography

Majorana fermions are a fascinating medium for discovering new phases of matter. However, the standard analytical tools are very limited in probing the non-perturbative aspects of interacting Majoranas in more than one dimensions. Here, we employ the holographic correspondence to determine the specific heat of a two-dimensional interacting gapless Majorana system. To perform our analysis we first describe the interactions in terms of a pseudo-scalar torsion field. We then allow fluctuations in the background curvature thus identifying our model with a $(2+1)$-dimensional Anti-de Sitter (AdS) geometry with torsion. By employing the AdS/CFT correspondence, we show that the interacting model is dual to a $(1+1)$-dimensional conformal field theory (CFT) with central charge that depends on the interaction coupling. This non-perturbative result enables us to determine the effect interactions have in the specific heat of the system at the zero temperature limit.

cond-mat.str-el↗

arXiv2019

Seeing topological edge and bulk currents in time-of-flight images

Here we provide a general methodology to directly measure the topological currents emerging in the optical lattice implementation of the Haldane model. Alongside the edge currents supported by gapless edge states, transverse currents can emerge in the bulk of the system whenever the local potential is varied in space, even if it does not cause a phase transition. In optical lattice implementations the overall harmonic potential that traps the atoms provides the boundaries of the topological phase that supports the edge currents, as well as providing the potential gradient across the topological phase that gives rise to the bulk current. Both the edge and bulk currents are resilient to several experimental parameters such as trapping potential, temperature and disorder. We propose to investigate the properties of these currents directly from time-of-flight images with both short-time and long-time expansions.

cond-mat.mes-hall↗

arXiv2019

Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model

Density functional theory maps an interacting Hamiltonian onto the Kohn-Sham Hamiltonian, an explicitly free model with identical local fermion densities. Using the interaction distance, the minimum distance between the ground state of the interacting system and a generic free fermion state, we quantify the applicability and limitations of the exact Kohn-Sham model in capturing the various properties of the interacting system. As a byproduct, this distance determines the optimal free state that reproduces the entanglement properties of the interacting system as faithfully as possible. The parent Hamiltonian of the optimal free state identifies a system that can determine the expectation value of any observable with controlled accuracy. This optimal entanglement model opens up the possibility of extending the systematic applicability of auxiliary free models into the non-perturbative, strongly-correlated regimes.

quant-ph↗

arXiv2019

Interaction distance in the extended XXZ model

We employ the interaction distance to characterise the physics of a one-dimensional extended XXZ spin model, whose phase diagram consists of both integrable and non-integrable regimes, with various types of ordering, e.g., a gapless Luttinger liquid and gapped crystalline phases. We numerically demonstrate that the interaction distance successfully reveals the known behaviour of the model in its integrable regime. As an additional diagnostic tool, we introduce the notion of "integrability distance" and particularise it to the XXZ model in order to quantity how far the ground state of the extended XXZ model is from being integrable. This distance provides insight into the properties of the gapless Luttinger liquid phase in the presence of next-nearest neighbour spin interactions which break integrability.

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