In many-body quantum systems, especially those with strong electronic correlations, the collective behavior of quasiparticles can give rise to emergent gauge degrees of freedom that are not imposed externally but generated intrinsically by the dynamics of the system. This paper proposes a unified theoretical framework for describing such self-generated gauge fields, here denoted as \(A_{\mu}^{\text{eff}}\), that arise naturally in quantum matter. We formulate the conditions under which the internal degrees of freedom of a material can spontaneously form a gauge structure, and we derive the effective action for the emergent gauge field in terms of the microscopic variables. The formalism is applied to a variety of strongly correlated systems, including spin liquids, fractional quantum Hall states, and high-temperature superconductors, illustrating how \(A_{\mu}^{\text{eff}}\) modifies the low-energy excitations and leads to novel observable phenomena. Furthermore, we discuss the potential of these emergent interactions to serve as platforms for discovering new artificial fundamental forces, thereby opening a route toward Nobel Prize–level physics.
In many-body quantum systems, especially those with strong electronic correlations, the collective behavior of quasiparticles can give rise to emergent gauge degrees of freedom that are not imposed externally but generated intrinsically by the dynamics of the system. This paper proposes a unified theoretical framework for describing such self-generated gauge fields, here denoted as (A_{\mu}^{\text{eff}}), that arise naturally in quantum matter. We formulate the conditions under which the internal degrees of freedom of a material can spontaneously form a gauge structure, and we derive the effective action for the emergent gauge field in terms of the microscopic variables. The formalism is applied to a variety of strongly correlated systems, including spin liquids, fractional quantum Hall states, and high-temperature superconductors, illustrating how (A_{\mu}^{\text{eff}}) modifies the low-energy excitations and leads to novel observable phenomena. Furthermore, we discuss the potential of these emergent interactions to serve as platforms for discovering new artificial fundamental forces, thereby opening a route toward Nobel Prize–level physics.
In many-body quantum systems the collective behavior of electrons can give rise to emergent phenomena that are not apparent from the underlying microscopic Hamiltonian. A particularly intriguing possibility is that the internal dynamics of a material can spontaneously generate a gauge potential A_mu^eff that couples to the electronic degrees of freedom in a manner formally identical to a conventional electromagnetic gauge field. This paper develops a theoretical framework for such self-generated gauge fields (SGGF) in quantum matter. Starting from a generic Hubbard-type model with long-range interactions, we derive an effective action for the fermions after integrating out high-energy modes. The resulting low-energy theory contains a covariant derivative D_mu = partial_mu - i A_mu^eff, where A_mu^eff emerges from the collective spin and charge fluctuations. We analyze the symmetry properties of the emergent field, show that it can acquire a mass gap or remain gapless depending on the underlying lattice geometry and interaction strength, and discuss the conditions under which it leads to novel topological responses. In particular, we identify a mechanism by which a chiral spin liquid state induces a Chern–Simons term for A_mu^eff, thereby realizing a fractional quantum Hall response without external magnetic fields. The possibility of realizing SGGF in cold atom simulators and in twisted bilayer graphene is highlighted. We conclude that the discovery of self-generated gauge fields opens a new avenue for engineering artificial fundamental interactions in solid-state platforms and for probing the interplay between topology and strong correlations.
In this work we propose that some strongly correlated quantum materials can spontaneously generate an effective geometrical structure described by a metric tensor g_{μν}^{eff}. Unlike engineered metamaterials or external spacetime analogues, this emergent geometry arises intrinsically from the many‑body quantum state. We develop a theoretical framework that connects the low‑energy effective action of fermionic quasiparticles to a curved‑space Dirac equation, with curvature determined self‑consistently by the electronic density and interaction parameters. The resulting geometry influences transport, optical, and topological properties, suggesting a novel platform for exploring quantum gravity concepts in table‑top experiments.
Complex quantum materials often exhibit unexpected emergent phenomena that cannot be fully explained by conventional band theory or mean-field approximations. In this paper, we propose that within the microscopic lattice of such materials a hidden causal network can self-organize. This causal network, represented by a matrix C_{ij}, captures directional dependencies between local degrees of freedom that influence electronic transport, spin dynamics, and energy redistribution. By formulating a set of coupled equations that relate the causal matrix to observable transport coefficients, we demonstrate that the causal structure can be inferred from macroscopic measurements. This framework provides a unifying perspective linking matter, information, and causality, and offers a potential pathway toward engineering quantum materials with tailored transport characteristics. The idea of self-generated causal structure may also shed light on the emergence of complex quantum behavior in strongly correlated systems and point toward future Nobel‑level discoveries in quantum materials science.
In this paper we propose and analyze a framework for simulating internal gravitational dynamics within quantum materials. By engineering many‑body interactions in a condensed‑matter setting we are able to generate an effective metric tensor g_{\mu\nu}^{eff} that couples to quasiparticle excitations in a manner analogous to general relativity. The central novelty lies in the fact that the simulated gravity is not an external background field but rather a self‑consistent emergent phenomenon arising from the collective behavior of the underlying electrons and phonons. We develop a field‑theoretic description of the emergent metric, construct a concrete model using a lattice of interacting fermions with tunable hopping amplitudes, and derive the effective action governing the quasiparticles. Numerical simulations demonstrate the appearance of curvature‑induced energy shifts and mode mixing that mirror gravitational red‑shift and lensing effects. The results suggest that quantum materials can serve as tabletop laboratories for probing the interplay between matter and spacetime, potentially offering new insights into the unification of quantum theory and gravitation.
Quantum many‑body systems exhibit a wealth of collective phenomena that cannot be inferred from the microscopic dynamics alone. In this work we introduce the concept of Self‑Emergent Law Dynamics (SELD) to describe how complex quantum systems spontaneously generate local effective laws that govern their own long‑time behavior. The central hypothesis is that, given a high‑dimensional Hilbert space and a Hamiltonian with local interactions, coarse‑graining over microscopic degrees of freedom can produce a position‑dependent effective Lagrangian L_eff(x) that captures the emergent dynamics of observable modes. We develop a theoretical framework to derive L_eff(x) from the underlying microscopic Hamiltonian, discuss the role of quantum entanglement and symmetry breaking, and propose experimental signatures that can be tested on quantum simulators. The paper outlines potential breakthroughs in understanding the emergence of physical laws, the design of self‑organized quantum devices, and new routes to simulate high‑energy physics phenomena.
Gauge theories and topological phases play a fundamental role in different areas of physics. The first ones are at the basis of the Standard Model in the field of particle physics, describing the electroweak and strong interactions through a non-Abelian gauge theory. In condensed matter and statistical physics, gauge theories arise as low-energy effective descriptions of strongly correlated phenomena, such as quantum spin liquids and quantum Hall effect. In this realm there is a strong connection with topological phases and order, as emergent gauge fermions and bosons often describe collective excitations of new exotic states of matter of spin models. The discretization on a lattice is a possible way of dealing with the strongly coupled nature of these theories, due to the fact that this formulation at finite volume provides natural regularizing cut-offs, i.e. the lattice size and spacing. This allows for the investigation of different non-perturbative properties both numerically and analytically. Despite the success of these methods, there are various aspects which remain intractable due to the sign or complex action problems, like the out of equilibrium real time evolution or the analysis of quantum chromodynamics with finite chemical potential. In this respect, quantum simulators of many-body systems to simulate high energy physics arise as promising alternatives to face these problems in the near future. They are quantum systems that can be controlled and used to simulate more complicated systems, whose properties could not be analysed with classical computational, experimental or theoretical tools. In the last decades, there has been a huge development in the fields of quantum optics and atomic physics, allowing for the realization highly precise and controllable platforms by means of trapped ions, superconducting circuits, Rydberg atoms and ultracold atoms in optical lattices. This work of Thesis is part of these fields and has different purposes, all of them connected with the study of gauge theories and topological phases. Firstly, we want to develop a reformulation of lattice gauge theories in terms of gauge invariant fields, in a way to deal solely with physical variables directly in the action. Among several possible advantages, a crucial point is that this can be particularly helpful for the construction of consistent approximation schemes, such as mean-field theories, in order to understand and capture some of the physical features of the theory and make the mean-field approximation consistent with the Elitzur theorem, stating that a local gauge symmetry can not be spontaneously broken. As a second point, we face the problem of simulating higher dimensional gauge theories with ultracold atoms. One of the challenges in more than one dimension is indeed the realization of plaquette interaction terms in the Hamiltonian of lattice gauge theories: these can be engineered through four correlated hoppings in perturbation theory, or by means of constrained hoppings in the dual formulation. In this respect, our main target is to set up an ultracold atomic platform generating the plaquette term in two dimensions using only two correlated hoppings, and protecting gauge invariance through angular momentum conservation. The last point we address in the Thesis is related to the analysis of particles moving in static background gauge potentials, i.e. when the considered gauge field has no dynamical term in the action of the system. Indeed, the dynamics of quantum particles in the presence of static gauge fields gives rise to intriguing physical phenomena. In particular, using ultracold atom setups, the realization of artificial gauge potentials can be used to investigate the physics of topological semimetals, such as Weyl or Dirac type. In the last ten years, a lot of attention has been paid to their characterization, due to the appearence of clear theoretical predictions and very well-controlled experimental techniques. We investigate here the relation between topological phase transitions and van Hove singularities, i.e. the discontinuities in the energy derivative of the density of states, in three-dimensional gapless systems. In such materials, topological phase transitions can be defined by changes of the topological invariants of the Fermi sheets, happening at specific singular points. Moreover, Fermi surface singularities result in the presence of the so-called van Hove points. We then present a general argument to relate topological phase transitions and van Hove singularities, and show observable consequences that are related to the transport properties of the system. We exemplify our argument in Weyl systems by analyzing the three-dimensional Hofstadter model for various commensurate fluxes, which offers the opportunity to consider different kinds of Weyl metals and to understand the features of their density of states.