Project description
Solving the sign problem in lattice gauge theories
The sign problem in lattice gauge theories (LGTs) remains a major challenge in computational physics, especially in higher dimensions. Traditional Monte Carlo methods struggle with this issue, limiting the study of strongly correlated systems in realistic settings. While projected entangled pair states (PEPS) have shown promise in lower-dimensional systems, their application in higher dimensions remains underexplored. In this context, the ERC-funded OverSign project aims to leverage a fundamental analogy between PEPS and gauge theories to overcome these limitations. By developing new methods, the project seeks to provide an efficient framework for studying non-perturbative models, particularly in quantum chromodynamics, advancing both theoretical and computational approaches.
Objective
Tensor networks, and particularly projected entangled pair states (PEPS), are special quantum many-body states that describe strongly-correlated systems well due to their entanglement structure. They have been successfully applied in various scenarios and recently to lattice gauge theories (LGTs) where they outperformed conventional Monte-Carlo calculations and overcame the sign problem in some examples, but mostly in single-space dimensions due to limitations of tensor network methods. A fundamental analogy between PEPS and gauge theories suggests that PEPS are suitable for studying LGTs and that gauge symmetry, often seen as complicating the numerics, can help in overcoming the sign problem and perform efficient tensor network computations in higher dimensions. The overarching goal of this project is to use this analogy in analytical and numerical ways, aiming to (1) analytically devise a comprehensive new formalism for LGT PEPS and the physics they describe by allowing one to construct the optimal PEPS to be used as variational ansatz states when combined with numerical techniques; (2) devise numerical methods for studying LGTs with such PEPS thanks to the analogy, based on sign problem-free variational Monte-Carlo; (3) apply these methods numerically to challenging, non-perturbative models, culminating in SU(3) in 3+1-D, with finite fermionic density, towards quantum chromodynamics. This is expected to overcome the sign problem of such models, thus closing an important, challenging and long-standing gap in the field of non-perturbative physics in general, and gauge theories in particular. The developed methods can be generalized for studying real-time dynamics of quantum field theories, models of quantum gravity, thermal quantum field theories and many other puzzling questions. They will also advance the parallel contemporary approach to LGT - quantum simulations and computations - as some open problems are shared by both approaches.
Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
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Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
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Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2023-COG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
91904 JERUSALEM
Israel
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