Quantum materials exhibit a wealth of emergent phenomena that arise from the complex interplay of electron correlations, spin dynamics, lattice vibrations, and external perturbations. Conventional analyses attribute observed responses to changes in the conventional spatial dimensions (x, y, z) and to well‑known order parameters such as magnetization, polarization, or superconducting gap. In this work we propose a new conceptual framework in which the response functions of quantum matter are expanded to include a hidden internal variable, denoted xi, that encapsulates an additional degree of freedom not captured by the spatial coordinates. The central hypothesis is that many observed anomalies, including unconventional superconductivity, quantum spin liquids, and topological phase transitions, can be understood as manifestations of a hidden dimensional response (HDR) mechanism. We formulate the response function R as a function of (x, y, z, xi), derive its implications for symmetry properties, and discuss possible experimental signatures that could confirm the existence of xi. This framework offers a unified viewpoint for interpreting a broad class of phenomena and suggests new avenues for material design and discovery.
Quantum materials exhibit a wealth of emergent phenomena that arise from the complex interplay of electron correlations, spin dynamics, lattice vibrations, and external perturbations. Conventional analyses attribute observed responses to changes in the conventional spatial dimensions (x, y, z) and to well‑known order parameters such as magnetization, polarization, or superconducting gap. In this work we propose a new conceptual framework in which the response functions of quantum matter are expanded to include a hidden internal variable, denoted xi, that encapsulates an additional degree of freedom not captured by the spatial coordinates. The central hypothesis is that many observed anomalies, including unconventional superconductivity, quantum spin liquids, and topological phase transitions, can be understood as manifestations of a hidden dimensional response (HDR) mechanism. We formulate the response function R as a function of (x, y, z, xi), derive its implications for symmetry properties, and discuss possible experimental signatures that could confirm the existence of xi. This framework offers a unified viewpoint for interpreting a broad class of phenomena and suggests new avenues for material design and discovery.
The concept of additional spatial dimensions has long been invoked to explain phenomena in high‑energy physics and cosmology. In this work we propose a fundamentally different paradigm: the presence of a hidden temporal coordinate within the response functions of quantum materials. We argue that the intrinsic dynamics of electrons, phonons, and collective excitations are governed not only by the observable laboratory time t but also by an auxiliary time parameter a_h that is not directly accessible to conventional measurement. This hidden time coordinate manifests itself in the structure of the Green's functions and in the evolution of many‑body states, leading to observable consequences such as anomalous dispersion, non‑Markovian relaxation, and time‑crystalline behaviour. We develop a formalism that incorporates the hidden time into the standard path‑integral and operator approaches, derive modified equations of motion, and discuss potential experimental signatures in ultrafast spectroscopy. The framework suggests that quantum materials can serve as a laboratory for exploring higher‑dimensional temporal physics, opening pathways for discovering new time‑related phases and for achieving unprecedented control over quantum dynamics.
The conventional description of solid state systems relies on spatial coordinates and a single temporal parameter that governs the evolution of quantum states. In this work, we propose that quantum materials exhibit a hidden, internal time coordinate that is distinct from the laboratory clock and is intrinsically linked to the quantum degrees of freedom. By extending the Hilbert space to include a hidden time operator τ, we derive a modified dynamical equation that couples the standard time t with τ. The resulting framework predicts novel spectral features, altered transport behavior, and unique nonlinear optical responses that can be accessed via ultrafast measurement techniques. The presence of a hidden time dimension offers a new perspective on temporal symmetries in condensed matter physics and opens pathways toward discovering previously unobserved time-dependent phenomena. This theoretical insight has the potential to lead to transformative advances and could be considered Nobel Prize worthy.
In strongly correlated quantum systems, the presence of conserved quantities beyond the obvious symmetries often leads to unexpected robustness of certain phases and excitations. We propose a systematic framework to search for hidden conserved operators, denoted Q_h, that commute with the full Hamiltonian H of a complex material. The core idea is that such hidden conservation laws may underpin anomalously stable states that defy conventional classification, potentially opening new avenues for topological quantum computation and material design. We formulate the problem as a constrained eigenvalue optimization, derive analytic expressions for candidate Q_h in representative lattice models, and introduce an iterative operator construction algorithm that exploits the algebraic structure of the spin, fermionic, and bosonic operators involved. By applying the method to a set of benchmark systems—spin chains with next‑nearest‑neighbour interactions, Hubbard‑type models with spin–orbit coupling, and coupled spin‑boson lattices—we demonstrate the emergence of non‑trivial conserved operators that are not linear combinations of known symmetries. The discovery of these hidden laws not only clarifies the stability of exotic phases such as quantum spin liquids and fractional topological insulators but also suggests that a deeper symmetry principle may underlie many unexplained experimental observations. Finally, we discuss the implications of our findings for future theoretical developments and the pursuit of a Nobel‑level breakthrough in the field of quantum materials.
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.
This paper introduces the concept of Hidden Causal Order in Quantum Matter (HCOQM), a novel framework proposing that within strongly correlated quantum materials, a previously unrecognized causal structure exists, operating beneath the conventional, empirically-derived descriptions. We posit that this 'hidden' causality isn't simply a consequence of complex interactions, but a fundamental organizing principle. This framework seeks to provide a new classification of quantum phases, moving beyond traditional approaches based solely on measured properties. The core concept is represented by the notation [C(x)], where C(x) denotes the causal relationship at position x. While experimental validation remains a significant challenge, HCOQM offers a theoretical lens through which to interpret complex quantum phenomena and potentially unlock the discovery of entirely new quantum phases. The paper explores the theoretical underpinnings of HCOQM and outlines potential avenues for future investigation.
The Schrödinger equation is nearly a century old, yet we are still in the midst of uncovering the remarkable phenomena emerging in many-body quantum systems. From superconductivity to anyonic quasiparticles, nature consistently surprises with its rich self-organization. To elucidate and grasp this variety, it is paramount to understand the phases of matter that can occur in many-body ground states, as well as their emergent collective excitations. Of particular interest are topological phases of matter, characterized by exotic excitations or edge phenomena. There exist by now several universal frameworks for gapped systems, i.e., those with an energy gap above the ground state. However, in the last decade, a multitude of gapless quantum wires---effectively one-dimensional systems---have been reported to be topologically non-trivial. A framework for their understanding and classification is missing. In addition to ground state order---topological or otherwise---a more complete picture involves the properties of excitations above the ground state. Alas, little is known about excitations beyond the universal low-energy regime. In part, this is due to a lack of analytical and numerical methods able to describe excitations at finite energies, especially in strongly-interacting systems beyond one dimension. In this thesis, we address these issues: firstly, we build a general understanding of topological phases in one dimension, including both gapped and gapless cases. In particular, we unify previously studied examples into a single framework. Secondly, we develop a novel numerical method for obtaining spectral functions in two dimensions---these give direct insight into the properties of excitations and are moreover experimentally measurable. Using this numerical method, we uncover a variety of robust properties of excitations at finite energies. Part I of this thesis concerns gapped and gapless topological phases in one dimension. In Chapter 2, we first treat the case of non-interacting fermions. Therein, we review the known classification of gapped phases before extending it to the gapless case, showing that exponentially-localized Majorana zero modes can still emerge at the edge when the bulk is gapless. Interacting gapped phases are discussed in Chapter 3, with a focus on symmetry-protected topological order. These have already been classified; our contribution is to provide a non-technical review of this classification as well as showing that many paradigmatic model Hamiltonians can be related to one another. Finally, Chapter 4 introduces the notion of symmetry-enriched quantum criticality, which we propose as a framework for classifying gapless phases. The key message is that in the presence of symmetries, a universality class can divide into distinct phases, characterized by the symmetry action on the low-energy scaling operators. This includes gapless topological phases, with examples hiding in plain sight; we clarify their stability and reinterpret previously studied examples. Part II studies the excitations above the ground states of two-dimensional quantum spin models. The main object of our study is the dynamic spin structure factor; this type of spectral function is reviewed in the first part of Chapter 5. The second part of this chapter introduces a novel matrix-product-state-based algorithm to efficiently compute it, opening a new window on the dynamics of two-dimensional quantum systems. We benchmark this numerical method in Chapter 6 on the exactly-solvable Kitaev model---a paradigmatic topological model realizing a quantum spin liquid. By adding non-integrable Heisenberg perturbations, we identify the first unequivocal theoretical realization of a proximate spin liquid: the ground state becomes conventionally ordered, yet the high-energy spectral properties are structurally similar to those of the nearby Kitaev spin liquid. The latter agrees with aspects of recent inelastic neutron scattering experiments on alpha-RuCl3. In Chapter 7, we turn to one of the oldest models in many-body quantum physics: the spin-1/2 Heisenberg antiferromagnet on the square lattice. Despite its venerable history, there is still disagreement about the physical origin of high-energy spectral features which low-order spin wave theory cannot account for. We provide a simple picture for this strongly-interacting-magnon feature by connecting it to a simple Ising limit. Lastly, Chapter 8 discusses the stability of quasiparticles---collective excitations behaving like a single emergent entity, of which magnons are a prime example. These are often known to be stable at the lowest energies and are presumed to decay whenever this is seemingly allowed by energy and momentum conservation. However, we show that strong interactions can prevent this from happening. We numerically confirm this principle of avoided decay in the (slightly-detuned) Heisenberg antiferromagnet on the triangular lattice. Moreover, we can even identify its fingerprints in existing experimental data on Ba3CoSb2O9 and superfluid helium. In this thesis, we thus enlarge our understanding of quantum phases and their excitations. The identification of the key principles of gapless topological phases in one dimension calls for direct analogues in higher dimensions, waiting to be uncovered. With regard to the robust properties of the excitations identified in this thesis, we are hopeful that these can be extended into a theory of quasiparticle properties away from the universal low-energy regime.