Papers by Héctor Mejía-Díaz
We study the impact of the Gradient Flow on the topology in various models of lattice field theor... more We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility χ t is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates χ t even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ 2). This ongoing study is
arXiv (Cornell University), Mar 23, 2015
arXiv (Cornell University), Oct 29, 2015
arXiv (Cornell University), Oct 1, 2014
Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015), 2016
EPJ Web of Conferences, 2018
We study the impact of the Gradient Flow on the topology in various models of lattice field theor... more We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility Xt is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates Xt even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ2). This ongoing study is based on direct measurements of Xt in L × L lattices, at L/ξ ≃6.
Physical Review D, 2016
We consider quantum field theories with topological sectors, in Euclidean spacetime. These sector... more We consider quantum field theories with topological sectors, in Euclidean spacetime. These sectors are characterized by a topological charge Q ∈ Z, which is a functional of the field configuration. In infinite volume, the
Journal of Physics: Conference Series, 2015
We discuss the λφ 4 model in 2-and 3-dimensional non-commutative spaces. The mapping onto a Hermi... more We discuss the λφ 4 model in 2-and 3-dimensional non-commutative spaces. The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations. The numerical results reveal a phase where stripe patterns dominate. In d = 3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing. This "striped phase" also occurs in d = 2. For both dimensions we provide evidence that it persists in the simultaneous limit to the continuum and to infinite volume ("Double Scaling Limit"). This implies the spontaneous breaking of translation symmetry.
Acta Physica Polonica B Proceedings Supplement, 2015
Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing,... more Lattice QCD simulations tend to get stuck in a single topological sector at fine lattice spacing, or when using chirally symmetric quarks. In such cases computed observables differ from their full QCD counterparts by finite volume corrections, which need to be understood on a quantitative level. We extend a known relation from the literature between hadron masses at fixed and at unfixed topology by incorporating in addition to topological finite volume effects, also ordinary finite volume effects. We present numerical results for SU(2) Yang-Mills theory.
Journal of High Energy Physics, 2014
We present a non-perturbative study of the λφ 4 model on a non-commutative plane. The lattice reg... more We present a non-perturbative study of the λφ 4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large λ it contains a "striped phase", which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed noncommutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner theorem.
In Monte Carlo simulations with a local update algorithm, th e auto-correlation with respect to t... more In Monte Carlo simulations with a local update algorithm, th e auto-correlation with respect to the topological charge tends to become very long. In the extreme cas one can only perform reliable measurements within fixed sectors. We investigate approach es to extract physical information from such topologically frozen simulations. Recent result s in a set ofσ -models and gauge theories are encouraging. In a suitable regime, the correct value of s ome observable can be evaluated to a good accuracy. In addition there are ways to estimate the val ue of the topological susceptibility.
arXiv: Quantum Physics, 2016
This manuscript is in progress and the first version was removed by decision of the autors.
Proceedings of The 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014), 2015
Topologically restricted measurements in lattice sigma-models Models with Topological Sectors Cor... more Topologically restricted measurements in lattice sigma-models Models with Topological Sectors Correlation Function of the Topological Charge Density Topological Summation Summary (Simplest) example for topological sectors: 1d O(2) model (quantum mechanical scalar particle on a circle).
Proceedings of The 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015), 2016
Journal of Physics: Conference Series, 2017
The 2d Heisenberg model-or 2d O(3) model-is popular in condensed matter physics, and in particle ... more The 2d Heisenberg model-or 2d O(3) model-is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge Q can still be defined such that Q ∈ Z. It has generally been observed, however, that the topological susceptibility χt = Q 2 /V does not scale properly in the continuum limit, i.e. that the quantity χtξ 2 diverges for ξ → ∞
Few-Body Systems, 2017
The behavior of the two-electron quantum dot interacting with a uniform magnetic field is not ful... more The behavior of the two-electron quantum dot interacting with a uniform magnetic field is not fully understood yet. This lack of clarity arises from the fact that the mixed, spherical and cylindrical, coordinates do not allow the system to be separable. In this paper, we applied an standard variational method, with a physical recipe for choosing compact trial functions. In order to solve the six dimensional integrals necessary to compute the expectation value of the Hamiltonian, we used a Monte Carlo routine. The energy values obtained are in agreement with the ones presented in previous literature.
Annals of Physics, 2016
We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N −1) quantum f... more We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N −1) quantum field theories. These theories share important features with (3 + 1)-d QCD, such as asymptotic freedom and θ-vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N −1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic preparation of the ground state of the system, the real-time evolution of a false θ-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.
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Papers by Héctor Mejía-Díaz