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Concept

Free lattice

Publications associées (11)

Geometric Considerations in Lattice Programming

Moritz Andreas Venzin

We provide faster algorithms and fine-grained reductions for lattice problems in general norms. ...

EPFL2023

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications

Ngoc Khanh Karol Nguyen

We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Efficient protocols for oblivious linear function evaluation from ring-LWE

Juan Ramón Troncoso-Pastoriza

An oblivious linear function evaluation protocol, or OLE, is a two-party protocol for the function f (x) = ax + b, where a sender inputs the field elements a, b, and a receiver inputs x and learns f (x). OLE can be used to build secret-shared multiplicatio ...

IOS PRESS2022

Linear Flavour-Wave Theory of SU(N) Lattice Models with Arbitrary Irreducible Representations

Francisco Hyunkyu Kim

This thesis explores various approaches of studying the long-range colour order of antiferromagnetic SU(N) Heisenberg models with the linear flavour-wave theory (LFWT). The LFWT is an extension of the well-known SU(2) spin-wave theory to SU(N), and this se ...

EPFL2019

Homogeneous number of free generators

We address two questions of Simon Thomas. First, we show that for any n >= 3 one can find a four-generated free subgroup of SLn (Z) which is profinitely dense. More generally, we show that an arithmetic group Gamma that admits the congruence subgroup prope ...

Walter De Gruyter Gmbh2014

Fixed Point Property For Universal Lattice On Schatten Classes

The special linear group G = SLn(Z[x(1), ... , x(k)]) (n at least 3 and k finite) is called the universal lattice. Let n be at least 4, and p be any real number in (1, infinity). The main result is the following: any finite index subgroup of G has the fixe ...

American Mathematical Society (AMS)2013

Competition between three-sublattice order and superfluidity in the quantum three-state Potts model of ultracold bosons and fermions on a square optical lattice

Frédéric Mila

We study a quantum version of the three-state Potts model that includes as special cases the effective models of bosons and fermions on the square lattice in the Mott-insulating limit. It can be viewed as a model of quantum permutations with amplitudes J(p ...

2013

Competition between two- and three-sublattice ordering for S=1 spins on the square lattice

Frédéric Mila

We provide strong evidence that the S = 1 bilinear-biquadratic Heisenberg model with nearest-neighbor interactions on the square lattice possesses an extended three-sublattice phase induced by quantum fluctuations for sufficiently large biquadratic interac ...

2012

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

Frédéric Mila

We present a numerical study of the SU(3) Heisenberg model of three-flavor fermions on the triangular and square lattice by means of the density-matrix renormalization group and infinite projected entangled-pair states. For the triangular lattice we confir ...

2012

Three-Sublattice Ordering of the SU(3) Heisenberg Model of Three-Flavor Fermions on the Square and Cubic Lattices

Frédéric Mila

Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest- ...

2010

Isometry groups of non-positively curved spaces: Discrete subgroups

Nicolas Monod

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained after a detour throu ...

2009