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.
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.
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.
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 Aμeff, 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 Aμeff 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.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.
We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.
Quantum geometry - including both the quantum metric and Berry curvature - arises from the non-zero overlap of well-defined eigenstates and their adiabatic evolution across the Brillouin zone. It has revolutionized condensed matter physics and material science by explaining quantum Hall effects, establishing the modern theory of polarization, and enabling a systematic search for topological materials on a large scale. Yet, despite these advances, we lack a framework for leveraging quantum geometry in the strongly interacting regime. Bridging this gap is critical: if we can harness geometric responses in correlated metals, we stand to engineer desirable transport and optical properties using existing material platforms, thus bypassing the complex task of designing materials with tailored quantum geometry from scratch. In this thesis, we take steps toward such a framework. First, we analyze the resilience of topological boundary modes in the presence of electronic correlations, identifying when interactions preserve, diminish, or destroy boundary modes. Second, we reveal geometric fingerprints of fluctuations in magnetically ordered systems, tying the electric quantum metric to the formation of instabilities and chiral quasi-particle excitations. Third, we generalize quantum geometry to describe families of many-body wave functions, providing a new algorithm to compute state-manifold curvatures suited to interacting phases. Our approach combines analytical theory with numerical methods, including density functional theory and tensor-network simulations, and is supported by open-source software developed during the PhD. Together, these results advance the topological classification of interacting phases and extend quantum geometry from single-particle bands to correlation functions, providing tools to design materials and devices with targeted geometric responses.