255 research outputs found
Compact lattice U(1) and Seiberg-Witten duality: a quantitative comparison
It was conjectured some time ago that an effective description of the
Coulomb-confinement transition in compact U(1) lattice gauge field theory could
be described by scalar QED obtained by soft breaking of the N=2 Seiberg-Witten
model down to N=0 in the strong coupling region where monopoles are light. In
two previous works this idea was presented at a qualitative level. In this work
we analyze in detail the conjecture and obtain encouraging quantitative
agreement with the numerical determination of the monopole mass and the dual
photon mass in the vicinity of the Coulomb to confining phase transition.Comment: 14 pag, 5 figure
Dynamics of the entanglement spectrum in spin chains
We study the dynamics of the entanglement spectrum, that is the time
evolution of the eigenvalues of the reduced density matrices after a
bipartition of a one-dimensional spin chain. Starting from the ground state of
an initial Hamiltonian, the state of the system is evolved in time with a new
Hamiltonian. We consider both instantaneous and quasi adiabatic quenches of the
system Hamiltonian across a quantum phase transition. We analyse the Ising
model that can be exactly solved and the XXZ for which we employ the
time-dependent density matrix renormalisation group algorithm. Our results show
once more a connection between the Schmidt gap, i.e. the difference of the two
largest eigenvalues of the reduced density matrix and order parameters, in this
case the spontaneous magnetisation.Comment: 16 pages, 8 figures, comments are welcome! Version published in JSTAT
special issue on "Quantum Entanglement In Condensed Matter Physics
Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
We introduce a theoretical scheme for the analog quantum simulation of
long-range XYZ models using current trapped-ion technology. In order to achieve
fully-tunable Heisenberg-type interactions, our proposal requires a
state-dependent dipole force along a single vibrational axis, together with a
combination of standard resonant and detuned carrier drivings. We discuss how
this quantum simulator could explore the effect of long-range interactions on
the phase diagram by combining an adiabatic protocol with the quasi-periodic
drivings and test the validity of our scheme numerically. At the isotropic
Heisenberg point, we show that the long-range Hamiltonian can be mapped onto a
non-linear sigma model with a topological term that is responsible for its
low-energy properties, and we benchmark our predictions with
Matrix-Product-State numerical simulations.Comment: closer to published versio
Suppression of Kondo-assisted co-tunneling in a spin-1 quantum dot with Spin-Orbit interaction
Kondo-type zero-bias anomalies have been frequently observed in quantum dots
occupied by two electrons and attributed to a spin-triplet configuration that
may become stable under particular circumstances. Conversely, zero-bias
anomalies have been so far quite elusive when quantum dots are occupied by an
even number of electrons greater than two, even though a spin-triplet
configuration is more likely to be stabilized there than for two electrons. We
propose as an origin of this phenomenon the spin-orbit interaction, and we show
how it profoundly alters the conventional Kondo screening scenario in the
simple case of a laterally confined quantum dot with four electrons.Comment: 5 pages, 3 figures, submitted 05May201
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
This work explores the use of a tree tensor network ansatz to simulate the
ground state of a local Hamiltonian on a two-dimensional lattice. By exploiting
the entropic area law, the tree tensor network ansatz seems to produce
quasi-exact results in systems with sizes well beyond the reach of exact
diagonalisation techniques. We describe an algorithm to approximate the ground
state of a local Hamiltonian on a L times L lattice with the topology of a
torus. Accurate results are obtained for L={4,6,8}, whereas approximate results
are obtained for larger lattices. As an application of the approach, we analyse
the scaling of the ground state entanglement entropy at the quantum critical
point of the model. We confirm the presence of a positive additive constant to
the area law for half a torus. We also find a logarithmic additive correction
to the entropic area law for a square block. The single copy entanglement for
half a torus reveals similar corrections to the area law with a further term
proportional to 1/L.Comment: Major rewrite, new version published in Phys. Rev. B with highly
improved numerical results for the scaling of the entropies and several new
sections. The manuscript has now 19 pages and 30 Figure
Operator content of entanglement spectra in the transverse field Ising chain after global quenches
We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows us to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critical point
How do population movements fit within the framework of systemic risk?
Population movements are key elements shaping today's complex and interconnected societies. Movement of people underpins the circulation of capital, knowledge, ideas, culture, values and resources with systemic benefits but it also produces diverse risk implications. The varied and complex implications of human mobility (and immobility) are still poorly understood by existing systemic risk approaches. This literature review approaches human mobility from a more comprehensive and complex standpoint to understand how it fits within a wider framework of systemic risk. In this article, we explore the complementary ways in which movements matter for systemic risk considerations, namely as: 1) a dynamic force that shapes exposure, vulnerability and resilience to disasters across places and scales; 2) a feature and consequence of disasters that has the potential to amplify, extend and prolong the impacts of hazards, and 3) a lifeline for people and societies worldwide, whose disruption has significant implications on systemic risk globally. These considerations have important theoretical consequences for the integration of population movements in systemic risk frameworks, and they propose practical lessons learned for the disaster risk reduction arena. We conclude that human mobility should not be understood as a negative impact that must be prevented and mitigated but as a positive phenomenon which enablement and protection a will lead to positive resilience outcomes and the reduction of risks
Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
We investigate the use of matrix product states (MPS) to approximate ground
states of critical quantum spin chains with periodic boundary conditions (PBC).
We identify two regimes in the (N,D) parameter plane, where N is the size of
the spin chain and D is the dimension of the MPS matrices. In the first regime
MPS can be used to perform finite size scaling (FSS). In the complementary
regime the MPS simulations show instead the clear signature of finite
entanglement scaling (FES). In the thermodynamic limit (or large N limit), only
MPS in the FSS regime maintain a finite overlap with the exact ground state.
This observation has implications on how to correctly perform FSS with MPS, as
well as on the performance of recent MPS algorithms for systems with PBC. It
also gives clear evidence that critical models can actually be simulated very
well with MPS by using the right scaling relations; in the appendix, we give an
alternative derivation of the result of Pollmann et al. [Phys. Rev. Lett. 102,
255701 (2009)] relating the bond dimension of the MPS to an effective
correlation length.Comment: 18 pages, 13 figure
Boundary quantum critical phenomena with entanglement renormalization
We extend the formalism of entanglement renormalization to the study of
boundary critical phenomena. The multi-scale entanglement renormalization
ansatz (MERA), in its scale invariant version, offers a very compact
approximation to quantum critical ground states. Here we show that, by adding a
boundary to the scale invariant MERA, an accurate approximation to the critical
ground state of an infinite chain with a boundary is obtained, from which one
can extract boundary scaling operators and their scaling dimensions. Our
construction, valid for arbitrary critical systems, produces an effective chain
with explicit separation of energy scales that relates to Wilson's RG
formulation of the Kondo problem. We test the approach by studying the quantum
critical Ising model with free and fixed boundary conditions.Comment: 8 pages, 12 figures, for a related work see arXiv:0912.289
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